Question

Scott shaves his face every morning. For the last 200 days, he has cut himself 36 times. Last year, he went the entire month of August (31 days) without cutting himself. Just last week, he cut himself 3 days in a row. Which event is more unusual? I.e., which event has a lower probability of occurring?

Answer 1

This is the case of binomial distribution where,

P[ he cuts himself ] = p = 36/200 = 0.18

P[ he cuts himself thrice in a week ]

n = 7

We need to find P[ X = 3 ]

This implies that

P[ X = 3 ] = 0.0923

He cuts himself none in a months

n = 31

We need to find P[ X = 0 ]

This implies that

P[ X = 0 ] = 0.0021

Cutting not even once in a month of Aug has lesser probability than cutting thrice in week

which event has a lower probability of occurring?

Cutting not even once in a month of Aug has lesser probability