Question

How many samples of size 3 can be drawn from {2,4,6,8}

(a) with replacement?

(b) without replacement?

(c) What is the probability in (a) that the first draw will be 2?

(d) What is the probability in (b) that the draw will have a 2?

Answer 1

Size 3 can be drawn from {2,4,6,8}

(a) with replacement:

The number of samples that can be selected = 4 * 4 * 4 = 64

(b) without replacement:

The number of samples that can be selected = 4 * 3 * 2 = 24

(c)

Probability in (a) that the first draw will be 2:

The number of numbers that begin with 2 will be 1*4*4=16

Hence the required probability is:

(d)

Probability in (b) that the draw will have a 2:

The number of samples that will have a 2 = 4*3=12

Hence the required probability

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