Question

a ball contain 5 blue and 4 white ball.A person select two balls randomly from it. the probability that the balls are of same colour?​

Answer 1

Answer:

5C2+4C2 / 9C2 = 4/9. so probability that the balls are of same colour is 4/9

Answer 2

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Given:

• 5 blue balls and 4 white balls.
• 2 balls are randomly selected.

To Find:

• The probability that the balls are of same colour

Solution:

So according to the question, we need to find the probability that the balls selected are of same colour, i.e., either both are blue or both are white.

So, for a favourable result, we select 2 blue balls or 2 white ones.

=> $\bf{^5C_2 + ^4C_2}$

This means that we select 2blue balls from 5blue ones OR 2white balls from 4white ones. We used a '+' operator bcoz these actions can't happen simultaneously, i.e.,onky one is possible at a time.

However, total number of observations will be

=> $\bf{^9C_2}$

This is so, because we are choosing 2 balls from the 9 available ones.

Hence,

$\text{P(E) =} \dfrac{Favourable\:outcomes}{Total\:Outcomes}$

$\text{P(E) =} \dfrac{^5C_2 + ^4C_2}{^9C_2}$

$\text{P(E) =} \dfrac{10 + 6}{36} \:\:\:\:\:\:\:(^5C_2=10; ^4C_2=6; ^9C_2=36)$

$\text{P(E) =} \dfrac{16}{36}$

$\bf\text{P(E) =} \dfrac{4}{9}}$

Hope it helps!