Question

A monkey is to demonstrate that she recognizes colors by tossing one red, one black, and one white ball into boxes of the same respective colors, one ball to a box. If the monkey has not learned the colors and merely tosses one ball into each box at random, find the probabilities of the following results: a There are no color matches. b There is exactly one color match.

Answer 1

Answer:

(a) 0.3333 or 33.33%

(b) 0.5000 or 50.00%

Step-by-step explanation:

(a) With the first toss, there is a 2/3 chance that the monkey gets it wrong, if the monkey gets it wrong, there is a 1/2 chance it gets the second wrong, which guarantees that the last toss is also wrong. The probability is:

$P = \frac{2}{3}* \frac{1}{2}*1=0.3333$

(b) There are 6 possible outcomes for this experiment, there are three outcomes with exactly one match, (Red is correct, white is correct, black is correct). The probability is:

$P=\frac{3}{6}=0.5$