Question

A bag contains 6 white, 4 green and 10 yellow balls. Two balls are drawn at random. Find the probability that both will be yellow.

Answer 1

Final Answer : 9/38

STEPS :
1) We have,
10 Yellow balls :
We have to select two balls, find the probability that both of them are yellow.
Total no. of balls = 6+4+10= 20

2) Then,
Total No. of out comes ,n(S) = Selecting 2 balls out of 20 balls

$= \binom{20}{2} = \frac{20 \times 19}{2 \times 1} = 190$

No. of favourable outcomes, n(E) =
Selecting two yellow balls
$= \binom{10}{2} = \frac{10 \times 9}{2 \times 1} = 45$

3)Probability ,P = n(E)/n(S)

$= \frac{45}{190} = \frac{9}{38}$

Hence, Probability of getting both balls as Yellow is 9/38 .