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Zarrin [17]
2 years ago
7

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

Mathematics
1 answer:
Katen [24]2 years ago
3 0

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

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