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Q.

In class 10 A, there are 20 boys and 20 girls. In 10 B, there are 15 boys and 25 girls. One student is to be selected from each class.

(i) What is the probability of both being girls?
(ii) What is the probability of both being boys? And
(iii) What is the probability of one boy and one girl?

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a

3/16, 5/16 and 2/16

b

9/16, 7/16 and 1/2

c

4/15, 7/15 and 8/15

d

9/15, 7/15 and 9/15

answer is B.

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Detailed Solution

Given,
In the class 10 A
Boys = 20
Girls = 20
Total student in 10 A
20 boys + 20 girls = 40
In the class 10 B
Boys = 15
Girls = 25
Total student in 10 B
15 boys + 25 girls = 40
1st case we have probability P (both being Girl)
Girls in class 10 A + Girls in class 10 B
20 + 25 = 45
Then probability of girls of both section

= \frac{45}{80} = \frac{9}{16}

2nd case we have probability P (both being Boys)
Boys in class 10 A + Boys in class 10 B
20 + 15 = 35
Then probability of Boys of both section

\frac{35}{80} = \frac{7}{16}

3rd case we have probability of one boy and one girl,
= (one boy (10A) and one girl (10 B) + (one boy (10B) and one girl (10A))
=

[\frac{20}{40} \times \frac{25}{40} + \frac{20}{40} \times \frac{15}{40}]

The probability of one boy and one girl=

\frac{500}{1600} + \frac{300}{1600}

Probability of one boy and one girl =1/2
Option 2 is correct.

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