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

Answer:

a) $P(x > 2) = \frac{1}{6}$

b) $P(x < 5) = \frac{1}{3}$

c) 50 times

Step-by-step 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:

$P(x > 2) = \frac{2}{12}$

Simplify

$P(x > 2) = \frac{1}{6}$

Solving (b): P(x < 5)

First, list all outcomes of x

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

So, the probability is:

$P(x < 5) = \frac{4}{12}$

Simplify

$P(x < 5) = \frac{1}{3}$

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:

$P(x ) = \frac{3}{12}$

Simplify

$P(x ) = \frac{1}{4}$

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

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

$E(x) = \frac{1}{4} * 200$

$E(x) = 50$