Question

A recent study on serious car accidents involving male drivers aged 18-24 found that 50% of the accidents were caused by excessive speed, 30% of the accidents caused by mobile phone use and 10% of the accidents involved the driver speeding and using his mobile phone.

Hint: Use a Venn diagram to help answer the following questions about the serious car accidents

1. What is the probability that an accident was caused by speeding alone?

2. What is the probability that neither speeding nor mobile phone use were involved?

3. What is the probability that an accident was caused by speeding or mobile phone use?

4. If a driver was speeding, what is the probability that he was also using his mobile?

e) Are speeding and mobile use mutually exclusive events? Explain.              

f) Are speeding and mobile use independent events? Explain

Answer 1

a) P(speeding alone) = P(speeding) - P(speeding and using mobile) = 0.5 - 0.1 = 0.4

b) P(neither speeding nor mobile phone) = 1 - P(either speeding or mobile phone)

                                                                 = 1 - (0.5 + 0.3 - 0.1)

                                                                 = 1 - 0.7 = 0.3

c) P(speeding or mobile phone) = 0.5 + 0.3 - 0.1 = 0.7

d) P(using mobile | speeding) = P(using mobile and speeding)/P(speeding)

                                                = 0.1/0.5 = 0.2

e) P(speeding and using mobile) = 0.1

Since P(speeding and using mobile) 0. so the events speeding and mobile use are not mutually exclusive.

f) P(speeding) * P(using mobile) = 0.5 * 0.3 = 0.15

Since P(speeding and using mobile) P(speeding) * P(using mobile), so the events speeding and mobile use are not independent.