Answer to Question #178369 in Statistics and Probability for anithra

Question

A box consists of 100 balls in total, for which 20 are red balls, 35 are blue balls, the rest are green balls. Moreover, each one of the 100 balls has either the letter “X” or “Y” printed on it. In total, 40 balls have letter “X” printed on them. Among the balls with “Y” printed on them, 26 are green and 14 are red.

d) If two balls are chosen at random, without replacement, find the probability that one of the balls is red and the other one is blue in color. (3 marks)

e) If two balls are chosen at random, without replacement, find the probability that exactly one ball is blue in color, and exactly one ball has the letter “X” printed on it (can be the same ball or different balls)

Answer 1

d)

$P=\frac{20}{100}\cdot\frac{35}{99}=\frac{7}{99}$

e) The probability that exactly one ball is blue in color:

$P_1=\frac{35}{100}\cdot\frac{65}{99}=\frac{91}{396}$

The probability that exactly one ball has the letter “X”:

$P_2=\frac{40}{100}\cdot\frac{60}{99}=\frac{8}{33}$

 The probability that exactly one ball is blue in color, and exactly one ball has the letter “X”:

$P=P_1\cdot P_2=\frac{91}{396}\cdot\frac{8}{33}=\frac{182}{3267}$