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. P(AnB)

b. P(B|A)

c.
`P(A^I|B)`

d. P(A or B)

e.
`P(B^I or A)`

Explanation:

Since A= driver is under 25 years old (1)

B = driver has received a speeding ticket (2)

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

this simple means the intersection of both set, which can be written as

P(AnB)

b. The probability a driver who is under 25 years old has received a speeding ticket.

This is a conditional probability, probability that B will occur given that A as occur.

P(B|A)

c. the probability a driver who has received a speeding ticket is 25 years or older.

`P(A^I|B)`

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

P(A or B)

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

`P(B^I or A)`