Question

From a bag containing 6 pink and 8 orange balls, 8 balls are drawn at random. The probability that 5 of
them are pink and the rest are orange is?​

Answer 1

℅℅Question :

From a bag containing 6 pink and 8 orange balls, 8 balls are drawn at random. What is the probability that 5 of

them are pink and the rest are orange?

Answer :

The probability that 5 of them are pink and the rest are Orange is 0.11 approx

Given :

No.of pink balls = 6

No.of orange balls = 8

No.of balls drawn at random = 8

To find :

The probability that 5 of them are pink and the rest are Orange

Solution :

We have to apply the concept of Combination here :

Total no.of balls = 6+8 = 14

Probability of the 5 balls being pink

= 6C5

Probability of the rest (8-5)=3balls being orange

= 8C3

Hence , favourable outcome = 6C5 × 8C3

Total no.of outcome = 14C8

Hence , The probability that 5 of them are pink and the rest are Orange is = ( 6C5 × 8C3 ) / 14C8

= ( 6 × 56 ) / 3003

= 336 / 3003

=0.11 approx

Therefore, The probability that 5 of them are pink and the rest are Orange is 0.11 approx

#SPJ1

Answer 2

Given:

From a bag containing 6 pink and 8 orange balls, 8 balls are drawn at random.

To find:

To find the probability that 5 of the balls drawn are pink and the rest are orange.

Solution:

Total balls in the bag = 6 pink + 8 orange

                                   = total of 14 balls

A total number of ways in which 8 balls are drawn at random = ways of selecting 8 balls from 14 balls.

Number of ways in which 8 balls are drawn at random from 14 balls = $\binom{14}{8}$

The number of ways in which 5 of the drawn balls are pink and other i.e. 3 remaining are orange = $\binom{6}{5} * \binom{8}{3}$ ( ways of selecting 5 pink balls from a total of 6 pink balls multiplied by ways of selecting 3 orange balls from a total of 8 orange balls.)

∴ The probability that 5 of them are pink and the rest are orange is : $\frac{Favourable outcomes}{Total outcomes}$

= $\frac{\binom{6}{5} * \binom{8}{3}}{\binom{14}{8}}$

= $\frac{6*56}{3003}$

= $\frac{112}{1`001}$

Answer:

The probability that 5 of the total balls drawn are pink and the rest are orange is :  $\frac{112}{1`001}$