Question

A 12-sided solid has equal-sized faces numbered 1-12

a. Find P(number greater than 10).

b.Find P(number less than 5)

c. If the 12-sided solid is rolled 200 times, how many times would you expect either a 4, 6, or 9 to be rolled?

Answer 1

a)
`P(x > 2) = (1)/(6)`

b)
`P(x < 5) = (1)/(3)`

c) 50 times

Explanation:

Given

`S = \{1,2,3,4,5,6,7,8,9,10,11,12\}`

Solving (a): P(x > 10)

First, list all outcomes of x

`x = \{11,12\}` --- 2 outcomes

So, the probability is:

`P(x > 2) = (2)/(12)`

Simplify

`P(x > 2) = (1)/(6)`

Solving (b): P(x < 5)

First, list all outcomes of x

`x = \{1,2,3,4\}` --- 4 outcomes

So, the probability is:

`P(x < 5) = (4)/(12)`

Simplify

`P(x < 5) = (1)/(3)`

Solving (c): Expected outcome of 4, 6 or 9 in a roll of 200

We have:

`n = 200`

First, list all outcomes of x

`x = \{4,6,9\}` --- 3 outcomes

So, the probability is:

`P(x ) = (3)/(12)`

Simplify

`P(x ) = (1)/(4)`

The expected number of rolls (E(x)) is calculated as:

`E(x) = P(x) * n`

`E(x) = (1)/(4) * 200`

`E(x) = 50`