Question

For this problem, involving a weighted die, assume that the outcomes 1 through 4 are equally likely, that the outcomes 5 through 6 are equally likely, and that outcome 1 is 3 times as likely as outcome 5.

(1) What probability should be assigned to rolling a 4?


(2) What probability should be assigned to rolling a 6?

Answer 1

a.
`(3)/(14)`

b.
`(1)/(14)`

Explanation:

We are given that a die is rolled

Let x bet the cases in favor of 5.

Number of cases in favor of 6=x

Then according to question

Number of cases in favor of 1=3x

Number of cases in favor of 2=3x

Number of cases in favor of 3=3x

Number of cases in favor of 4=3x

Sum of total cases=
`x+x+3x+3x+3x+3x=14x`

Probability of getting 5 =
`(x)/(14x)=(1)/(14)`

Probability of getting 1=
`(3x)/(14x)=(3)/(14)`

1.We have to find probability should be assigned to rolling a 4.

The probability of getting =
`(3)/(14)`

2.We have to find the probability of rolling 6.

The probability of getting 6=
`(1)/(14)`