Question

A certain class has ‘s’ students. If a student is picked at random, the probability of picking a boy is 8/13. If the class has 24 boys, what is the value of ‘s’?

Answer 1

p(b)=8/13

probability of boys = no. of boys/ total students

8/13=24/s

8s=24×13

s=3×13

s=39

Answer 2

SOLUTION

GIVEN

• A certain class has ‘s’ students.

• A student is picked at random

• The probability of picking a boy is 8/13.

• The class has 24 boys

TO DETERMINE

The value of s

EVALUATION

Here it is given that certain class has ‘s’ students.

Total number of possible outcomes = s

The class has 24 boys

Let A be the event that of picking a boy

Then total number possible outcomes for the event A is 24

The probability

= P(A)

$\displaystyle \sf{ = \frac{24}{s} }$

So by the given condition

$\displaystyle \sf{ \frac{24}{s} = \frac{8}{13} }$

$\displaystyle \sf{ \implies 8s = 24 \times 13}$

$\displaystyle \sf{ \implies s = \frac{24 \times 13}{8} }$

$\displaystyle \sf{ \implies s = 36}$

FINAL ANSWER

Hence the required value of s = 39

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