Question

The article "Should You Report That Fender-Bender?"† reported that 7 in 10 auto accidents involve a single vehicle. Suppose 11 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 five involve multiple vehicles?

Answer 1

Answer:

Given,

Binomial distribution P(X = x) = nCx*p^x*q^(n-x)

n = 11

p = 7/10

= 0.7

q = 1 - p

= 1 - 0.7

= 0.3

a)

To give P(X = 4) = 11C4*0.7^4*0.3^(11-4)

= 11C4*0.4^4*0.3^7

= 330*0.4^4*0.3^7

= 0.0018

b)

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 11C0*0.7^0*0.3^11 + 11C1*0.7^1*0.3^10 + 11C2*0.7^2*0.3^9 + 11C3*0.7^3*0.3^8 + 11C4*0.7^4*0.3^7

= 0.3^11 + 11*0.7*0.3^10 + 55*0.7^2*0.3^9 + 165*0.7^2*0.3^9 + 330*0.7^4*0.3^7

= 0.000002 + 0.00005 + 0.0005 + 0.0016 + 0.0173

= 0.0195

c)

P(X = 5) = 11C5*0.7^5*0.3^(11-5)

= 462*0.7^5*0.3^6

= 0.0566