Question

2.         An experiment consists of rolling a single die one time. A teacher asked her students to

find the probability that the die will land on an even number or a number that is a divisor

of 6. Leona said, "It's 3/6 + 4/6 = 7/6, since three out of the six numbers on the die are

even and there are four numbers on the die that go into six." Discuss what is wrong with

Leona’s reasoning. (4 points)

Answer 1

The experiment is rolling a die one time. Therefore, the sample space is given by,

Let A be a event that the die will land on even number, therefore,

Let B be the event that the number is divisor of 6, therefore,

Then the event C = A or B means the union of A and B, thus,

Therefore, the probability that the die will land on an even number or a number that is a divisor of 6 is actually the probability of event C, i.e.

Leona's result was obviously wrong because the probability she obtained was greater than 1, which can never happen. The probability will always lie between 0 and 1. Also she didn't took care of the intersection between the two events.