Class 11

In a class, 5 \% of the boys and 10 \% of the girls have an IQ of more than 150 . In this class, 60 \% of the students are boys. If a student is selected at random and found to have and IQ of more than 150, find the probability that the student is a boy.

Let, I : students having IQ more than 150 B : Boys in the class G: Girls in the class We want to find $P(B \mid I)$ i.e. probability that selected student having IQ greater than 150 is a boy...

read more

In a certain college, 4 \% of boys and 1 \% of girls are taller than 1.75 meters. Furthermore, 60 \% of the students are girls. If a student is selected at random and is taller than 1.75 meters, what is the probability that the selected student is a girl?

Let, T :students taller than $1.75$ B: Boys in class G: Girls in class We want to find $P(G \mid T)$, i.e. probability that selected taller is a girl $\begin{array}{l} \mathrm{P}(\mathrm{G} \mid...

read more

A company manufactures scooters at two plants, A and B. plant A produces 80 \% and plant B produces 20 \% of the total product. 85 \% of the scooters produced at pant A and 65 \% of the scooters produced at plant B are of standard quality. A scooter produced by the company is selected at random, and it is found to be of standard quality. What is the probability that it was manufactured at plant A?

Let S : Standard quality We want to find $\mathrm{P}(\mathrm{A} \mid \mathrm{S})$, i.e. probability that selected standard scooter is from plant A $\mathrm{P}(\mathrm{A} \mid...

read more

In a bulb factory, three machines, A, B, C, manufacture 60 \%, 25 \% and 15 \% of the total production respectively. Of their respective outputs, 1 \%, 2 \% and 1 \% are defective. A bulb is drawn at random from the total product, and it is found to be defective. Find the probability that it was manufactured by machine C.

Let D : Bulb is defective We want to find $P(C \mid D)$, i.e. probability that the selected defective bulb is manufactured by $C$ $\mathrm{P}(\mathrm{C} \mid \mathrm{D})=\frac{\mathrm{P}(\mathrm{C})...

read more

An anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shots are 0.4,0.3,0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?

Given:Let $A, B, C$ and $D b e$ first second third and fourth shots whose probability of hitting the plane is given i.e, $\mathrm{P}(\mathrm{A})=0.4, \mathrm{P}(\mathrm{B})=0.3,...

read more

A town has two fire-extinguishing engines, functioning independently. The probability of availability of each engine when needed is 0.95 . What is the probability that
(i) neither of them is available when needed?
(ii) an engine is available when needed?

Given: Let $A$ and $B$ be two fire extinguishing engines. The probability of availability of each of the two fire extinguishing engines is given i.e., $\mathrm{P}(\mathrm{A})=0.95$ and...

read more

An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X. 8 out of 100 parts may be defective. Similarly, 5 out of 100 parts of Y may be defective. Calculate the probability that the assembled product will not be defective.

Given: $X$ and $Y$ are the two parts of a company that manufactures an article. Here the probability of the parts being defective is given i.e, $\mathrm{P}(\mathrm{X})=\frac{8}{100}$ and...

read more

Neelam has offered physics, chemistry and mathematics in Class XII. She estimates that her probabilities of receiving a grade A in these courses are 0.2,0.3 and 0.9 respectively. Find the probabilities that Neelam receives
(i) all A grades
(ii) no A grade

Given : let $A, B$ and $C$ represent the subjects physics,chemistry and mathematics respectively ,the probability of neelam getting $A$ grade in these three subjects is given i.e, $P(A)=0.2,...

read more

How many permutations can be formed by the letters of the word ‘VOWELS’, when (i) there is no restriction on letters; (ii) each word begins with E; (iii) each word begins with O and ends with L; (iv) all vowels come together; (v) all consonants come together?

Answer : (i) There is no restriction on letters The word VOWELS contain 6 letters. The permutation of letters of the word will be 6! = 720 words. Each word begins with Here the position of letter E...

read more

A customer forgets a four-digit code for an automated teller machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6, 9. Find the largest possible number of trials necessary to obtain the correct code.

Answer : Given: code consists of digits 3, 5, 6, 9. To find: the largest possible number of trials necessary to obtain the correct code. The customer remembers that this 4 digit code consists of...

read more