Question

Suppose a box contains 6 Red, 2 Green and 4 White balls. Two balls are selected at random without replacement. X is the number of red and Y is the number of green balls in the sample. Find P(X=0∣Y=1)

Answer 1

The probability P(X=0·Y=1), which is the probability of not selecting a red ball given that one green ball has been selected, is 4/11.

Step-by-step explanation:

To find the probability P(X=0·Y=1), we must first understand that X=0 represents the event of not selecting a red ball, and Y=1 represents the event of selecting exactly one green ball when we pick two balls from the box at random without replacement. Since we are given that one of the balls selected is green, we can ignore the other green ball when calculating the probability of not selecting a red ball, as there are only two green balls in the box. Our task is then to find the probability of picking a white ball, given the first ball picked was green.

There are a total of 12 balls in the box initially: 6 red, 2 green, and 4 white. Therefore, the probability of selecting a white ball after already selecting one green ball is the number of white balls divided by the remaining total number of balls after one green ball is removed. This gives us 4 white balls divided by 11 remaining balls, resulting in a probability of 4/11.

Thus, the probability P(X=0·Y=1) of selecting no red balls and exactly one green ball is 4/11.