A hat contains 4 marbles: one red, one blue, one orange, and one green. Two marb

Question

A hat contains 4 marbles: one red, one blue, one orange, and one green. Two marbles are selected at random without replacement from the hat. Answer parts a through d. a) Determine the number of points in the sample space. There are points in the sample space. b) Determine the probability of selecting exactly 1 red marble. The probability is (Simplify your answer.) c) Determine the probability of selecting at least 1 marble that is not red. The probability is (Simplify your answer.) d) Determine the probability of selecting no blue marbles. The probability is (Simplify your answer.)

Explanation / Answer

Solution:-

a) The number of points in the sample space is 12.

n = 4, x = 2

The number of points in the sample space = 4 × 3 = 12

b) The probability of selecting exactly one red marbles = 0.25.

Number of red marbles = 1

The number of ways of selecting one marbles = 1 × 3C1

The probability of selecting one marbles = 3/12 = 0.25

c) The probability of selecting at least one marble that is not red = 0.50

Number of non red marbles = 3

The number of ways of selecting at least one marble that is not red = 1 × 3C1 + 3C1 × 2C1 = 3 + 6 = 9

The probability of selecting at least one marble that is not red = 9/12 = 0.75

d) The probability of selecting no blue marbles = 0.50

Number of ways of selecting no blue marbles = 3C1 × 2C1 = 6

The probability of selecting no blue marbles = 6/12 = 0.50

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