Adam bought a package of marbles and sorted all of them by color as shown in the

Question

Adam bought a package of marbles and sorted all of them by color as shown in the graph below. 5) 5 4 3 Marbles 2 1 0 Number of red white black yellow a) What was the total number of marbles in the package? b) If one marble was selected at random, find the probability it was black, red or yellow? c) If two marbles were selected at random, with replacement, find the probability one of the two marbles was red? d) If two marbles were selected at random, without replacement, find the probability neither marble was red or black? e) If two marbles were selected at random, with replacement, find the probability one of the two marbles was blue?

Explanation / Answer

a)

Following table show the frequency distribution of marbles:

hence, total number of marbles is 12.

b)

Out of 12 marbles, 8 are red, black or yellow so the required probability is

P(red, black or yellow) = 8/12 = 0.6667

c)

Out of 12 marbles, 2 are red. Since marbles are selected with replacement so required probability is

P(one is red) = (2/12)* (2/12) = 0.0278

d)

Out of 12 marbles, 9 are not red or black.

The requried probabiity is C(9,2) / C(12,2) = 0.5455

e)

Since no marble is blue so required probability is

P(one is blue) = 0

Color Number of marbles Red 2 White 4 Black 1 Yellow 5 Total 12

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