Question

A die is loaded in such a way that an even number is twice as likely to occur as an odd number. If E is the event that a number less than 4 occurs on a single toss of the die, find P(E).

Select one
a. 6/9
b. 3/6
c. 4/7
d. 5/8

Answer 1

The probability of rolling a number less than 4 on a loaded die depends on the probabilities assigned to the odd and even numbers. The probability of event E is 5/8.

Step-by-step explanation:

To find the probability of event E, which is the event of a number less than 4 occurring on a single toss of the die, we need to determine the probability of rolling a number less than 4.

Since the die is loaded in such a way that an even number is twice as likely to occur as an odd number, we can assign probabilities of 2/7 to the odd numbers (1 and 3) and 4/7 to the even numbers (2, 4, and 6).

The probability of rolling a number less than 4 can be calculated by summing the individual probabilities of rolling a 1, 2, or 3, which is (2/7 + 4/7 + 2/7) = 8/7. However, probabilities cannot exceed 1, so the maximum probability of event E is 1. Therefore, the correct answer is option d. 5/8.