Question

A bag contains 5 white, 7 red, and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.

Answer 1

The probability that none of the drawn balls is red is 2/91.

Step-by-step explanation:

To find the probability that none of the drawn balls is red, we need to determine the total number of ways to draw 3 balls from the bag and the number of ways to draw 3 balls without any red balls.

There are a total of 15 balls in the bag, so the number of ways to draw 3 balls without any red balls is the number of ways to draw 3 balls from the 5 white and 3 black balls.

The number of ways to draw 3 balls without replacement is given by the combination formula: nCr = n! / (r!(n-r)!).

So, the probability that none of the drawn balls is red is:

P(none is red) = number of ways to draw 3 balls without any red balls / total number of ways to draw 3 balls

P(none is red) = (5C3 * 3C0) / 15C3

P(none is red) = (10 * 1) / 455

P(none is red) = 2 / 91