A date in September is chosen at random. What is the probability of choosing an even number or a multiple of 5?

3/5

Step-by-step explanation:

there are 30 days in September.

Set of even-numbered dates = {2, 4, 6, 8, …, 30}

Set of dates that are multiples of five = {5, 10, 15, … 30}

Number of dates that are even-numbered = 15

Number of dates that are multiples of five= 6

Probability of choosing an even number = 15/30 = 1/2

Probability of choosing a multiple of 5 = 6/30 = 1/5

Note that the two events are mutually inclusive, i.e. we can have a date that is both even and a multiple of 5. There are 3 such dates i.e. {10, 20, 30}.

So, probability of choosing both an even number and a multiple of 5 = 3/30 = 1/10

Therefore, probability of choosing an even number OR a multiple of 5

= 1/2 + 1/5 - 1/10= 3/5