Question

A recent survey revealed that 60% of drivers use their seat belts. A sample of 10 drivers on a major road is selected. Calculate the probability that no more than 3 drivers are wearing seat belts

Answer 1

Answer on Question #82320 – Math — Statistics and Probability

Question

A recent survey revealed that 60% of drivers use their seat belts. A sample of 10 drivers on a major road is selected. Calculate the probability that no more than 3 drivers are wearing seat belts

Solution

Let $X$ be the number of drivers that are wearing seat belts (among 10 selected drivers). Then we need to calculate $P(X \leq 3)$.

We have

$$\begin{array}{l} P (X \leq 3) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3), \\ P (X = k) = \binom{10}{k} p^{k} (1 - p)^{10 - k}, \end{array}$$

where $p = 0.6, k = 0,1,2,3$.

We get

$$\begin{array}{l} P (X \leq 3) = 0.4^{10} + 10 * 0.6^{1} * 0.4^{9} + \frac{10 * 9}{2} 0.6^{2} * 0.4^{8} + \frac{10 * 9 * 8}{2 * 3} 0.6^{3} * 0.4^{7} \\ = 0.05476. \end{array}$$

Answer: 0.05476.

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