Roth is a computer-consulting firm. The number of new clients that they have obt

Question

Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.

Number of

New Clients

Probability

0

0.05

1

0.10

2

0.15

3

0.35

4

0.20

5

0.10

6

0.05

Let X be the number of new clients:

Events:

A: X £ 3

B: X > 3 (This is the correct answer)

C: 1 < X £ 6

Question:

1. What is the sample Space?

2. Calculate:

i. P(AC)

ii. P(A È B)

iii. P(AC)

iv. P(A È C)

Number of

New Clients

Probability

0

0.05

1

0.10

2

0.15

3

0.35

4

0.20

5

0.10

6

0.05

Explanation / Answer

1. Sample Space S = {0,1,2,3,4,5,6}

2. ) P(A and C) = P(X<=3 and 1<X<6) = P(1< X <=3) = 0.15+0.35 = 0.6

ii) P(A or B) = P(X<=3) + P(X>3) = 0.05 + 0.10+0.15+0.35+0.20+0.10+0.05 = 1

iii) P(A and C) = P(X<=3 and 1<X<=6) = P(1< X <=3) = 0.15+0.35 = 0.6

iv) P(A or C) = P(X<=3 or 1<X<=6) = P(0<=X<=6) = 1

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