G An urn contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected one at a time, replacing each ball after selecting it. What is the probability that fewer than 2 of the selected balls are red given that exactly 2 of the selected balls are yellow? Give your answer as a decimal rounded to four places (i. e. X.)

The probability that fewer than 2 of the selected balls are red given that exactly 2 of the selected balls are yellow is 0.7840.

Step-by-step explanation:

The balls in the urn are:

R = red balls = 3

Y = yellow balls = 2

B = blue balls = 5

The probability of drawing a red ball is, .

The probability of drawing a yellow ball is, .

The probability of drawing a blue ball is, .

Five balls are drawn from the urn with replacement.

The conditional event of selecting less than 2 red balls given that exactly 2 yellow balls have already been selected is same as selecting less than 2 red balls in 3 draws.

The event of the number of red balls selected follows a binomial distribution with parameters n = 3 and .

The probability mass function of a Binomial distribution is:

Compute the probability of selecting less than 2 red balls in 3 draws as follows:

P (R < 2) = P (R = 0) + P (R = 1)

Thus, the probability that fewer than 2 of the selected balls are red given that exactly 2 of the selected balls are yellow is 0.7840.

idn

step-by-step explanation: