Question

QUESTIONS
There are two friends A and B giving the Maths Quiz. The probability of qualifying A is 1/7 and
the probability of qualifying B is 1/5. What is the probability that only one of them qualifies?​

Answer 1

Given:

There are two friends A and B giving the Maths Quiz. The probability of qualifying A is 1/7 and the probability of qualifying B is 1/5.

To find:

What is the probability that only one of them qualifies?​

Solution:

Let,

"P(A)" → the event that friend A qualifies

"P( A' )" → the event that friend A does not qualify

"P(B)" → the event that friend B qualifies

"P( B' )" → the event that the friend B does not qualify

Here we have

P(A) = $\frac{1}{7}$

∴ P( A' ) = $1 - \frac{1}{7} = \frac{7-1}7} = \frac{6}{7}$

and

P(B) = $\frac{1}{5}$

∴ P( B' ) = $1 - \frac{1}{5} = \frac{5-1}5} = \frac{4}{5}$

Now,

The probability that only one of them qualifies is,

= [P(A) × P( B' )] + [P( A' ) × P(B)]

= $[\frac{1}{7} \times \frac{4}{5} ] + [\frac{6}{7} \times \frac{1}{5} ]$

= $[\frac{4}{35} ] + [\frac{6}{35} ]$

= $\frac{10}{35}$

= $\bold{\frac{2}{7}}$

Thus, the probability that only one of them qualifies is → $\underline {\bold{\frac{2}{7}}}$.

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