For teenage drivers 14 have been issued speeding tickets 8 f

For teenage drivers, 14% have been issued speeding tickets, 8% for going through a red light and 5% both.

A) What percent of teens have not been issued either ticket?

B) are the 2 types of tickets dijoint?

C) are the 2 types of tickets independent events?

Solution

Let

s = speeding
R = red light

a)

P(S U R)\' = 1 - [P(S) + P(R) - P(S n R)]

= 1 - (0.14 + 0.08 - 0.05)

= 0.83 [ANSWER]

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b)

NO. If they are disjoint, P(S n R) = 0, but it is 0.05.

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c)

No. If they are independent, then

P(S n R) = P(S) P(R)

However,

P(S) P(R) = 0.14*0.08 = 0.0112

However, P(S n R) = 0.5.

Hence, THEY ARE NOT INDEPENDENT.