1) What is the value of w2? (2) What is the value of w1? (3) What is the value of w3?

Question

For this problem, assume that 2, 6, 5, and 4 are equally likely, a 1 is three times as likely as a 4, and a 3 is four times as likely as a 1.
(1) What is the value of w2?

(2) What is the value of w1?

(3) What is the value of w3?

Answer 1

Important Information given in the math problem as follows:

The probabilities of rolling 2, 4, 5, 6 are equal.

The probability of rolling a 1 is three times the probability of rolling a 4.

The probability of rolling a 3 is four times the probability of rolling a l.

Hint: The sum of the probabilities of all possible outcomes is 1.

How to solve the math question?

1. Set up an equation where the sum of all probabilities equals 1.
2. Solve for the unknow probability.

Step 1

Define the probability of rolling a 4

Let w4 be the probability of rolling a 4.

Step 2

The probability of rolling a 2, 5, or 6 is also w4.

The probability of rolling a 1 is w1 = 3 times w4.

The probability of rolling a 3 is w3 = 4w1 = 4(3w4) = 12w4

Step 3

The sum of the probabilities of all outcomes is 1.

w1 + w2 + w3 + w4 + w5 + w6 = 1

w4+w4+w4+w4 + 3w4 + 12w4 =1

Step 4

Combine like terms:

20 w4 = 1

Divide by 20:

w4 = 1 divided by 20 = 1/20

Step 5

Since w2 = w4:

w2 = 1/20

Step 6

Since w1 = 3w4:

w1 = 3 times 1/20 = 3/20

Step 7

Since w3 = 12w4:

w3 = 12 times 1/20 = 12/20 = 3/5

Solution:

The probabilities are w2 = 1/20, w1 = 3/20 and w3 = 3/5

I hope this information is useful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an Amazing Day. Doris H. 5/4/2025