# Probability Essay Example

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## Probability

Question 1

Question 2

If a member of staff is selected at random what is the probability that:

1. They are in the most senior grade.

P=102/200=0.51

1. They are in the least senior grade.

P= 40/200=0.2

1. They are Male.

P(M)=138/200=0.69

1. They are Female.

P(F)=62/200=0.31

1. .They are in the most senior grade given that they are Female

P=40/200=0.2

1. They are Female given that they are in the most senior grade.

P=40/200=0.2

1. They are in the least senior grade given that they are Male.

P=29/200=0.145

.They are Male given that they are in the least senior grade (h)

P=29/200=0.145

Question 3

Question 4

 Promoted Not Promoted
1. What is the probability that a family will own both a US car and a non US car?

P(Owns a U.S car AND non U.S car)

30/200=0.15

1. Use the marginal probabilities to compare US and non US car ownership.

1. What is the probability a family owns a car?

P(Owns non-US car but not non-US car AND Owns US car but not non-US car AND Owns both US car and non-US car).

10/200+150/200+30/200

0.05+0.75+0.15=0.95

If a family owns a US car, what is the probability that it also owns a non US car?iv.

150/200+30/200=0.9

1. If a family owns a non US car, what is the probability that it also owns a US car?

10/200+30/200=0.2

1. Are US car and non US car ownership independent? Explain your answer.

Let A be US car

Let B be non-US car

P(A AND B)=30/200=0.15

P(A) .P(B)150/200×180/200=1.64

P(A AND B) not equal P(A) .P(B) so the event A and B are not independent

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