probability question in description

Question

This is the question: ----- scott shaves his face every morning. for the last 200days he cuts himself 36times. A.) find the probability he will cut himself tomorrow. B.) find the probability he will cut himself two days in a row. C.) Last year scott when the entire month of august (31days) without cutting himself. Just last week, he cut himself three days in a row. Which of those two events is more unlikely to occur? Show work please.

Answer 1

We start by assuming that getting cut is a completely random process---just like flipping a perfect coin or a perfect 6-sided die.

 

We observe that he cuts himself 36 out of every 200 shaves.  Thus, the probability of cutting on any single day is 36 / 200 = 0.18  (18%)

From this the probability of NOT cutting himself is 0.88  (The probability of all possible outcomes must add up to 1)

 

For random events,  the probability of getting N occurrences is the probability of EACH occurrence raised to the Nth power.  Example, flipping a coin---probability of heads is 0.5, so 2 heads in a row is 0.5^2 = .25

 

The probability of 3 cuts in a row:   0.18^3 = 0.00583

 

The probability of 31 days of NO cuts is the 31st power of the probability of ONE day with no cuts