Question

I need help ASAP

A bag contains 6 red 5 blue and 4 green identical balls. 3 balls are drawn from the bag at random without replacement. calculate correct to 3 d.p the probability:
i) that the balls are of the same colour
ii) a ball from each of the 3 colours is drawn. ​

Answer 1

To solve this problem, we first need to determine the total number of ways to select 3 balls out of the 15.

Total number of ways to select 3 balls out of 15 = 15C3 = (15*14*13)/(3*2*1) = 455

i) To calculate the probability that the 3 balls drawn are of the same color, we need to find the number of ways we can select 3 balls of the same color and divide it by the total number of ways to select 3 balls.

Number of ways to select 3 red balls = 6C3 = (6*5*4)/(3*2*1) = 20

Number of ways to select 3 blue balls = 5C3 = (5*4*3)/(3*2*1) = 10

Number of ways to select 3 green balls = 4C3 = (4*3*2)/(3*2*1) = 4

Total number of ways to select 3 balls of the same color = 20+10+4 = 34

Probability that the 3 balls drawn are of the same color = 34/455 ≈ 0.0747 (correct to 3 decimal places)

ii) To calculate the probability that a ball from each of the 3 colors is drawn, we need to find the number of ways we can select 1 ball of each color and divide it by the total number of ways to select 3 balls.

Number of ways to select 1 red ball, 1 blue ball and 1 green ball = 6*5*4 = 120

Probability that a ball from each of the 3 colors is drawn = 120/455 ≈ 0.2637 (correct to 3 decimal places)

Therefore, the probabilities are:

i) Probability that the balls are of the same colour = 0.0747 (correct to 3 decimal places)

ii) Probability that a ball from each of the 3 colors is drawn = 0.2637 (correct to 3 decimal places)

Explanation:

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