Question

birthdays a year has 365 days, excluding leap years. use 365 days in a year in the following calculations and assume each birthday is equally likely: enter your answer as a decimal rounded to 4 decimal places. (a) determine the probability that a randomly selected person has a birthday on the 30th day of a month. so find p(birth day = 30)

Explanation:

Step1: Determine total and favorable outcomes

Total number of days in a year is 365. Number of 30 - th days in a year: Some months have a 30th day. There are 11 months that can have a 30th day (all except February which has 28 or 29 days in non - leap and leap years respectively). So the number of 30th days in a year is 11.

Step2: Calculate probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Here, the number of favorable outcomes (having a birthday on the 30th day of a month) is 11 and the total number of outcomes (total days in a year) is 365. So $P(\text{birth day}=30)=\frac{11}{365}$.

Answer:

$0.0301$