Chapter 9.7, Problem 66E

To determine

if the statement, “Rolling a number less than 3 on a normal six-sided die has a probability of $\frac{1}{3}$ . The complement of this event is rolling a number greater than 3, which has a probability of $\frac{1}{2}$ ” is true or false.

Answer to Problem 66E

False

Explanation of Solution

The given statement is false because the sum of the probabilities of an event and its complement is always 1 which is not the case here.

Here, the problem is that the complement of the event “Rolling a number less than 3” is the event “Rolling a number greater than or equal to 3” which has the probability $\frac{2}{3}$

And here the sum of both probabilities is 1.