Question

Consider the following events for a driver selected at random from a general population.

A = driver is under 25 years old                                              (1)

B = driver has recieved a speeding ticket                             (2)

Translate each of the following phrases into symbols.

(a) The probability the driver is under 25 years old and has recieved a speeding ticket.

(b) The probability a driver who is under 25 years old has recieved a speeding ticket.

(c) The probability a driver who has recieved a speeding ticket is 25 years or older.

(d) The probability the driver is under 25 years old or has recieved a speeding ticket.

(e) The probability the driver is under 25 years old or has not recieved a speeding ticket.

Answer 1

a) Notice the word "and" so your answer is
P(A and B)

(b) Notice the given condition of being under 25 years old so your answer is the probability of B given A or
P(B | A) .

(c) Notice that the given is the speeding ticket and you want the driver to NOT be under 25 so your answer is the probability of not A given B or
P(Ac | B)

(d) Notice the word "or" so your answer is
P(A or B)

(e) Notice again the "or" and the "has not received a speeding ticket" so your answer is the probability of not B or A, or
P(Bc or A)

Answer 2

1) P(A and B)

2) P(B|A)

3) P(Ac|B)

4) P(AUB)

5) P(AUBc)

Answer 3

a) Notice the word "and" so your answer is
P(A and B)

(b) Notice the given condition of being under 25 years old so your answer is the probability of B given A or
P(B | A) .

(c) Notice that the given is the speeding ticket and you want the driver to NOT be under 25 so your answer is the probability of not A given B or
P(Ac | B)

(d) Notice the word "or" so your answer is
P(A or B)

(e) Notice again the "or" and the "has not received a speeding ticket" so your answer is the probability of not B or A, or
P(Bc or A)

Answer 4

1) P(A and B)

2) P(B|A)

3) P(Ac|B)

4) P(AUB)

5) P(AUBc)