Question

2. The probability that a car will come to a complete stop at a particular stop sign is 0.4. Assume that the next four cars
arrive at the stop sign are independent of one another. Find each of the following probabilities:
a) None of the four cars come to a complete stop?

Answer 1

Answer:

$P(X = 0) = 0.1296$

Step-by-step explanation:

This can be solved using the binomial distribution because the cars arriving at the stop are independent of each other. This means we will use:

$P(X = x) = \binom{n}{x} p^{x} q^{n - x}$

Where p is the probability of success, q = 1 - p is the probability of failure and n is the number of cars sampled.

p = 0.4

q = 0.6

n = 4

Therefore,

$P(X = 0) = \binom{4}{0} 0.4^{0} 0.6^{4}$

This is equal to

$P(X = 0) = 1 \times 1 \times 0.1296$

$P(X = 0) = 0.1296$