Question 8.112

81. Suppose you select 10 people at random. Find the probability of each event below:

  1. At least one match in the day of the week that they were born
  2. At least one match in the day of the month that they were born (assume 31 days per month)
  3. At least one match in the day of the year that they were born

81.

(a) Because there are only 7 days in the week and 10 people are chosen at random, the probability that there is a match is 100% (certainty).

(b) Assuming 31 days in a month, the probability we seek is

or approximately 80%.

(c) Assuming 365 days in a year, the probability we seek is

or approximately 12%.