Question

Every morning there is an 70% chance that I get to the bus on times. if each morning is independent of the others, what is the probability that I get to the bus on times at least 4 times in 5 days?

a 0.04437
b. 0.3915
c. 0.05220
d 0.5282
e 0.9657

Answer 1

d 0.5282

Explanation:

Given the following :

Probability of getting to the bus on time = 70% = P = probability of success = 0.7

(1 - p) = probability of failure = 0.3

Number of trials(n) = 5 days

Number of sucesses (r) = atleast 4 days : >= 4

This is a binomial probability problem

P(r) = nCr × P^r × (1 - P)^(n - r)

P(X >=4) = P(4) + P(5)

P(4) = 5C4 × (0.7)^4 × (0.3)^1 = 0.36015

P(5) = 5C5 × (0.7)^5 × (0.3)^0 = 0.16807

P(4) + P(5) = 0.36015 + 0.16807 = 0.52822