Suppose a box contains 16 marbles, 5 are red, 4 are blue, and 7 are yellow. Find

Question

Suppose a box contains 16 marbles, 5 are red, 4 are blue, and 7 are yellow. Find the requested probabilities. Round your answers to 3 significant digits* .

(a) If two marbles are selected with replacement, what is the probability that one is red and the other is yellow?
P({red and yellow} or {yellow and red}) =

(b) If two marbles are selected without replacement, what is the probability that one is red and the other is yellow?
P({red and yellow} or {yellow and red}) =

(c) If 5 marbles are selected without replacement, what is the probability that they are all yellow?
P(yellow and yellow and yellow and yellow and yellow) =

...............................................
*Significant Digits: Here are some probabilities expressed to 3 significant digits. You start counting digits from left to right starting with the first non-zero digit.

0.123      0.0123      0.0120      0.00123      0.102      0.350      0.300

Explanation / Answer

a) P({red and yellow} or {yellow and red}) = (5/16)*(7/16)+(5/16)*(7/16) = 0.273

b) P({red and yellow} or {yellow and red}) = (5/16)*(7/15)+(7/16)*(5/15) = 0.292

c) P(all yellow) = (7/16)*(6/15)*(5/15)*(4/14)*(3/13) = 0.004

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