We are given the word ‘$ASSASSINATION$’. The total letters in the given word $ = 13$. Number of vowels in the given word $ = 6$. Number of consonants in the given word $ = 7$. Then, the sample space...
If is the probability of an event, what is the probability of the event ‘not ’.
We are given that, $\frac{2}{{11}}$ is the probability of an event $A$, $P(A) = \frac{2}{11}$ Then, the probability of ‘not $A$’ is $P\left( {not{\text{ }}A} \right) = 1-P\left( A \right)$ $ = 1 -...
Three coins are tossed once. Find the probability of getting (ix) at most two tails
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed three times then the sample space contains, $S{\text{ }} = {\text{...
Three coins are tossed once. Find the probability of getting (vii) Exactly two tails (viii) no tail
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed three times then the sample space contains, $S{\text{ }} = {\text{...
Three coins are tossed once. Find the probability of getting (v) no head (vi) 3 tails
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed three times then the sample space contains, $S{\text{ }} = {\text{...
Three coins are tossed once. Find the probability of getting (iii) at least 2 heads (iv) at most 2 heads
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed three times then the sample space contains, $S{\text{ }} = {\text{...
Three coins are tossed once. Find the probability of getting (i) heads (ii) heads
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed three times then the sample space contains, $S{\text{ }} = {\text{...
A fair coin is tossed four times, and a person win Rs for each head and lose Rs for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.
When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$. Here, coin is tossed four times then the sample space contains, $S{\text{ }} = {\text{...
There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?
We are given that, there are four men and six women on the city council. So, the total members in the council $\; = {\text{ }}4{\text{ }} + {\text{ }}6{\text{ }} = {\text{ }}10$. Thus, the sample...
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) (ii)
The possible outcomes when a die is thrown are $1, 2, 3, 4, 5$ and $6$. Then the sample space is, $S = \left\{ {\left( {1,1} \right){\text{,}}\left( {1,2} \right),\left( {1,3} \right),\left( {1,4}...
A card is selected from a pack of 52 cards. (c) Calculate the probability that the card is an ace (d) Calculate the probability that the card is a black card
(c) A card is selected from a pack of $52$ cards. Suppose $B$ be the event of drawing an ace. We have four aces in a pack. So, $n\left( B \right) = {\text{ }}4$. $P\left( {Event} \right) =...
A card is selected from a pack of cards. (a) How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades.
We know that in a deck there are $52$ cards. (a) The event of number of points in the sample space = $52$. Therefore, $n\left( S \right){\text{ }} = {\text{ }}52$. (b) suppose, $A$ be the event of...
A die is thrown, find the probability of following events: (iii) A number less than or equal to one will appear, (iv) A number more than will appear,
The possible outcomes when a die is thrown are $1, 2, 3, 4, 5$ and $6$. Then the sample space is, $S{\text{ }} = {\text{ }}\left\{ {1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6}...
A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to will appear,
The possible outcomes when a die is thrown are $1, 2, 3, 4, 5$ and $6$. Then the sample space is, \[S{\text{ }} = {\text{ }}\left\{ {1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6}...
A coin is tossed twice, what is the probability that at least one tail occurs?
A coin is tossed twice, what is the probability that at least one tail occurs? When a coin is tossed then the possible outcomes are either a Head \[\left( H \right)\] or Tail\[\left( T \right)\]....
Which of the following cannot be valid assignment of probabilities for outcomes of sample Space ?
Given assignment is (e) Condition (i): Each of the number $p\left( {{\omega _i}} \right)$ is positive and less than zero. Condition (ii): Sum of probabilities $ = {\text{ }}\left( {1/14}...
Which of the following cannot be valid assignment of probabilities for outcomes of sample Space ?
Given assignment is (c) Condition (i): Each of the number $p\left( {{\omega _i}} \right)$ is positive and less than zero. Condition (ii): Sum of probabilities $ = {\text{ }}0.1{\text{ }} + {\text{...
Which of the following cannot be valid assignment of probabilities for outcomes of sample Space ?
Given assignment is (a) Condition (i): Each of the value $p\left( {{\omega _i}} \right)$ is positive and less than zero. Condition (ii): Sum of probabilities $0.01{\text{ }} + {\text{ }}0.05{\text{...