Question

The article "Should You Report That Fender-Bender?"† reported that 7 in 10 auto accidents involve a single vehicle. Suppose 15 accidents are randomly selected. (Round your answers to five decimal places.)

(a) What is the probability that exactly four involve a single vehicle?

(b) What is the probability that at most four involve a single vehicle?

(c) What is the probability that exactly six involve multiple vehicles?

Answer 1

a)

Here, n = 15, p = 0.7, (1 - p) = 0.3 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 4)
P(X = 4) = 15C4 * 0.7^4 * 0.3^11
P(X = 4) = 0.00058

b)

Here, n = 15, p = 0.7, (1 - p) = 0.3 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 4).
P(X <= 4) = (15C0 * 0.7^0 * 0.3^15) + (15C1 * 0.7^1 * 0.3^14) + (15C2 * 0.7^2 * 0.3^13) + (15C3 * 0.7^3 * 0.3^12) + (15C4 * 0.7^4 * 0.3^11)
P(X <= 4) = 0 + 0 + 0.00001 + 0.00008 + 0.00058
P(X <= 4) = 0.00067

c)

Here, n = 15, p = 0.7, (1 - p) = 0.3 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 15C6 * 0.7^6 * 0.3^9
P(X = 6) = 0.01159