Exercise 15.1

### Two dice are rolled together. Find the probability o f getting such numbers on two dice whose product Is perfect square.

Solution: When two different dice are thrown, then total number of outcomes = 36. Let E be the event of getting the product of numbers, as a perfect square. These numbers are (1,1), (1,4), (2,2),...

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### When two dice are tossed together, find the probability that the sum o f the numbers on their tops Is less than 7.

Solution: When two different dice are thrown, the total number of outcomes = 36. Let E be the event of getting the sum of the numbers less than 7. These numbers are (1,1), (1,2), (1,3), (1,4),...

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### Two different dice are rolled simultaneously. Find the probability that the sum o f the numbers on the two dice Is 10.

Solution: When two different dice are thrown, the total number of outcomes = 36.   Let E1 be the event of getting the sum of the numbers on the two dice is 10. These numbers are (4 ,6), (5,5)...

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### A stash contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. In case almost certainly, one of the coins will drop out when the bank is flipped around, what is the likelihood that the coin

(I) will be a 50 p coin? (ii) won't be a ₹5 coin? Solution: Complete no. of coins = 100+50+20+10 = 180 P(E) = (Number of ideal results/Total number of results) (I) Total number of 50 p coin = 100 P...

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### Gopi purchases a fish from a shop for his aquarium. The retailer takes out one fish indiscriminately from a tank containing 5 male fish and 8 female fish (see Fig. 15.4). What is the likelihood that the fish taken out is a male fish?

Solution: The all out number of fish in the tank = 5+8 = 13 All out number of male fish = 5 P(E) = (Number of good results/Total number of results) P (male fish) = 5/13 = 0.38

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### A shot in the dark comprises of turning a bolt which stops pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 15.5), and these are similarly probable results. What is the likelihood that it will point at

(I) 8? (ii) an odd number? (iii) a number more noteworthy than 2? (iv) a number under 9? Solution: Complete number of potential results = 8 P(E) = (Number of great results/Total number of results)...

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### A bite the dust is tossed once. Discover the likelihood of getting

(I) an indivisible number; (ii) a number lying somewhere in the range of 2 and 6; (iii) an odd number. Solution: Complete potential occasions when a dice is tossed = 6 (1, 2, 3, 4, 5, and 6) P(E) =...

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### One card is drawn from a very much rearranged deck of 52 cards. Discover the likelihood of getting

(I) a lord of red tone (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the sovereign of jewels Arrangement: All out number of potential results = 52 P(E) = (Number of...

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### Five cards the ten, jack, sovereign, ruler and trick card, are very much rearranged with their face downwards. One card is then gotten up.

(I) What is the likelihood that the card is the sovereign? (ii) If the sovereign is drawn and set to the side, what is the likelihood that the subsequent card gotten is (a) an ace? (b) a sovereign?...

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### 12 flawed pens are inadvertently blended in with 132 great ones. It is unimaginable to simply take a gander at a pen and tell whether it is blemished. One pen is taken out aimlessly from this parcel. Decide the likelihood that the pen taken out is a decent one.

Solution: Quantities of pens = Numbers of blemished pens + Numbers of good pens ∴ Total number of pens = 132+12 = 144 pens P(E) = (Number of great results/Total number of results) P(picking a decent...

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### (I) A ton of 20 bulbs contain 4 blemished ones. One bulb is drawn indiscriminately from the part. What is the likelihood that this bulb is damaged?(ii) Suppose the bulb attracted (I) isn’t damaged and isn’t supplanted. Presently one bulb is drawn indiscriminately from the rest. What is the likelihood that this bulb isn’t deficient?

Solution: (I) Number of damaged bulbs = 4 The absolute number of bulbs = 20 P(E) = (Number of great results/Total number of results) ∴ Probability of getting a damaged bulb = P (deficient bulb) =...

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### A container contains 90 plates which are numbered from 1 to 90. On the off chance that one circle is drawn aimlessly from the crate, discover the likelihood that it bears

(I) a two-digit number (ii) an ideal square number (iii) a number distinguishable by 5. Solution: The complete number of plates = 90 P(E) = (Number of great results/Total number of results) (I)...

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### A kid has a kick the bucket whose six faces show the letters as given underneath:

The bite the dust is tossed once. What is the likelihood of getting (I) A? (ii) D? Solution: The complete number of potential results (or occasions) = 6 P(E) = (Number of ideal results/Total number...

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### Assume you drop a kick the bucket aimlessly on the rectangular locale displayed in Fig. 15.6. What is the likelihood that it will land inside the circle with breadth 1m?

Solution: To start with, compute the space of the square shape and the space of the circle. Here, the space of the square shape is the conceivable result and the space of the circle will be the...

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### A great deal comprises of 144 ball pens of which 20 are deficient and the others are acceptable. Nuri will purchase a pen in case it is acceptable, yet won’t accepting in case it is damaged. The retailer draws one pen indiscriminately and offers it to her. What is the likelihood that

(I) She will get it? (ii) She won't get it? Arrangement: The all out quantities of results for example pens = 144 Given, quantities of inadequate pens = 20 ∴ The quantities of non inadequate pens =...

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### (I) Complete the accompanying table: (ii) An understudy contends that ‘there are 11 potential results 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. In this way, every one of them has a likelihood 1/11. Do you concur with this contention? Legitimize your Solution:.

Solution: On the off chance that 2 dices are tossed, the potential occasions are: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3,...

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### A game comprises of throwing a one rupee coin multiple times and taking note of its result each time. Hanif wins if every one of the throws give a similar outcome i.e., three heads or three tails, and loses in any case. Ascertain the likelihood that Hanif will lose the game.

Solution: The absolute number of results = 8 (HHH, HHT, HTH, THH, TTH, HTT, THT, TTT) Absolute results in which Hanif will lose the game = 6 (HHT, HTH, THH, TTH, HTT, THT) P (losing the game) = 6/8...

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### A bite the dust is tossed twice. What is the likelihood that

(I) 5 won't come up one or the other time? (ii) 5 will come up in some measure once? [Hint : Throwing a bite the dust twice and tossing two dice at the same time are treated as the equivalent...

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### Which of the accompanying contentions are right and which are not right? Give purposes behind your Solution:.

(I) If two coins are thrown at the same time there are three potential results—two heads, two tails or one of each. In this manner, for every one of these results, the likelihood is 1/3 (ii) If a...

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### A marble is picked out at random from a box containing 5 red marbles, 8 white marbles and 4 green marbles. What is the probability that the marble picked out will be

(i) a red marble? (ii) a white marble? (iii) is not a green marble? Solution: The Total number of marbles in the box = 5+8+4 = 17 P(E) = (Number of favourable outcomes/ Total number of outcomes) (i)...

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### A ball is picked at random from a bag containing 3 red balls and 5 black balls. What is the probability that the ball picked up at random is

(i) a red ball? (ii) not a red ball? Solution: The total number of balls inside the bag = Number of red balls + Number of black balls So, the total no. of balls inside the bag = 5+3 = 8 As we know...

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### In a group of 3 students, it is given that the probability of 2 students not having the same birth date is 0.992. What is the probability that the 2 students have the same birth date?

Solution: Let E be the event wherein 2 students having the same birth date. A/Q Given, P(E) = 0.992 As we know, P(E)+P(not E) = 1 So, P(not E) = 1–0.992 = 0.008 ∴ The probability that the 2 students...

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### A bag contains only lemon flavored candies. Malini picked one candy from the bag without looking into it. What is the probability that she picked up

(i) a candy of orange flavor? (ii) a candy of lemon flavored? Solution: (i) As we know that the bag contains lemon-flavored candies only. So, The no. of orange flavored candies = 0 So, the...

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### If P(E) = 0.05, what is the probability of P(not E)?

Solution: We know that, P(E)+P(not E) = 1 A/Q It is given that, P(E) = 0.05 So, P(not E) = 1-P(E) Or, P(not E) = 1-0.05 ∴ P(not E) = 0.95

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### Which of the below mentioned values cannot be the probability of an event?

(A) 2/3 (B) -1.5 (C) 15% (D) 0.7 Solution: The probability of any event (E) must lie between 0 and 1 i.e. 0 ≤ P(E) ≤ 1. So, from the above options, only option (B) -1.5 cannot be the probability of...

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### Why tossing a coin is considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

Solution: Coin tossing is a fair way of deciding because the number of possible outcomes are only 2 i.e. either  it is a head or a tail. Since these two outcomes are an equally likely outcome,...

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### Which of the following experiments mentioned below have equally likely outcomes? Explain.

(i) A driver attempts to start a car. The car starts or does not start. (ii) A player tries to shoot a basketball. She/he shoots perfectly or misses the shot. (iii) A trial is made to a Solution: a...

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### Complete the statements given below:-

(i) The probability for any event E, P(E) + P(not E) ___________. (ii) The probability of an event that will never occur is __________. These events are called ________. (iii) The probability of an...

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