Question

Consider a sample space with 3 A’s and 2 B’s. Assume that each sample point is equally likely to be selected.

(a) What is the probability that a randomly selected set of 2 items will include all B’s?

(b) What is the probability that a randomly selected set of 3 items will include all A’s? 1

(c) What is the probability that a randomly selected set of 2 items will include 1 A and 1 B?

(d) What is the probability that a randomly selected set of 3 items will include 2 A’s and 1 B?

Answer 1

Total number of sample points = 3+2 = 5

Number of 'A's in the sample space = 3

Number of 'B' in the sample space = 2

(a) Probability that a randomly selected set of 2 items will include all B’s:

Number of ways of selecting 2 items from the 5: total sample points =

Number of ways of selecting 2 B's from 2 B's =

Probability that a randomly selected set of 2 items will include all B’s:

= Number of ways of selecting 2 B's from 2 B's / Number of ways of selecting 2 items from the 5: total sample points

= 1/10 = 0.1

Probability that a randomly selected set of 2 items will include all B’s = 0.1

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(b) Probability that a randomly selected set of 3 items will include all A’s

Number of ways of selecting 3 items from the 5: total sample points =

Number of ways of selecting 3 A's from 3 A's =

Probability that a randomly selected set of 3 items will include all A’s

= Number of ways of selecting 3 A's from 3 A's / Number of ways of selecting 3 items from the 5: total sample points

= 1/10 = 0.1

Probability that a randomly selected set of 3 items will include all A’s = 0.1

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(c) Probability that a randomly selected set of 2 items will include 1 A and 1 B

Number of ways of selecting 2 items from the 5: total sample points =

Number of ways of selecting 1 A from 3 A's =

Number of ways of selecting 1B from 2B's =

Probability that a randomly selected set of 2 items will include 1 A and 1 B =

(Number of ways of selecting 1 A from 3 A's x Number of ways of selecting 1B from 2B's) / Number of ways of selecting 2 items from the 5: total sample points

=(2 x 3) / 10 = 6/10 = 0.6

Probability that a randomly selected set of 2 items will include 1 A and 1 B = 0.6

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(d) probability that a randomly selected set of 3 items will include 2 A’s and 1 B

Number of ways of selecting 3 items from the 5: total sample points =

Number of ways of selecting 2 A from 3 A's =

Number of ways of selecting 1B from 2B's =

Probability that a randomly selected set of 3 items will include 2 A’s and 1 B

= (Number of ways of selecting 2 A from 3 A's x Number of ways of selecting 1B from 2B's ) / Number of ways of selecting 3 items from the 5: total sample points

= (3x2)/10 = 6/10 = 0.6

Probability that a randomly selected set of 3 items will include 2 A’s and 1 B = 0.6