Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. in a random sample of 12 drivers driving between 10pm and 3 am, find the probability that:
a) exactly two will be drunken drivers.
b) three or four will be drunken drivers.
c) at least 7 will be drunken drivers.
d) at most 5 will be drunken drivers.

(a) 0.28347

(b) 0.36909

(c) 0.0039

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

(a) Exactly two will be drunken drivers.

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

Using binomial we get

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.