Question

a bag contains 2 white and 3 red balls two balls are selected at random find the probability of getting one white and one red ball​

Answer 1

total possible outcomes=5

(1)no.of favourable event=2

P(one white ball)=2/5

(2)no.of favourable event=3

P(one red ball)=3/5.

Answer 2

The probability of getting one white and one red ball = 2/5

Given :

• A bag contains 2 white and 3 red balls

• Two balls are selected at random

To find :

The probability of getting one white and one red ball

Solution :

Step 1 of 3 :

Find total number of possible outcomes

The bag contains 2 white and 3 red balls

Total number of balls

= 2 + 3

= 5

Now two balls are selected at random

So total number of possible outcomes

$\displaystyle \sf = {}^{5} C_2$

= 15

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that of getting one white and one red ball

Total number of possible outcomes for the event A

$\displaystyle \sf = {}^{2} C_1 \times {}^{3} C_1$

= 2 × 3

= 6

Step 3 of 3 :

Find the probability

Hence the required probability of getting one white and one red ball

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{6}{15} }$

$\displaystyle \sf{ = \frac{2}{5} }$

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