Question

It is estimated that 78% of drivers use their turn signal.

Part A: What is the probability that exactly 3 drivers use their turn signal if a police
officer pulls over five drivers? (5 points)
Part B: What is the probability the next driver using their turn signal that the police
officer pulls over is the fifth driver? (5 points) (10 points)
I

Answer 1

A) 0.23

B) 0.14

Explanation:

Part A)
To solve this question, we'll have to use the Bernoulli formula.
The formula claims that the probability to get
`k` successes out of
`n` attempts is given by
`\binom{n}{k}p^k(1 - p)^(n - k)`.

In our case,
`n = 5`,
`k = 3`, and
`p = 0.78`.

Therefore, the probability that 3 out of the 5 drivers use their turn signal is

`\binom53 * 0.78^3 * 0.22^2 \to 0.23`

Part B)

We are told that the police officer pulled over 5 drivers, 3 of them using turn signals. In this part, we are asked "what is the probability that the 5th driver uses the turn signal and only 2 of the previous four drivers use turn signals?".

`0.78 * \binom42 * 0.78^2 * 0.22^(4-2)\\\to 0.14`