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A sixteen-sided number cube has the numbers 1 through 16 on each face. each face is equally likely to show after a roll. what is the probability that you will roll an even number or an odd prime number? round to the nearest thousandth.

a. 0.063
b. 0.813
c. 0.219
d. 0.875

2 Answers

1 vote
P(even number) = 8/16 = 1/2...sample space is 16, there are 8 even numbers (2,4,6,8,10,12,14,16)
P (odd prime number) = 5/16...sample space is 16, there are 5 odd primes (3,5,7,11,13)

P (both) = 1/2 + 5/16 = 8/16 + 5/16 = 13/16 = 0.8125 rounds to 0.813
User Sommmen
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4 votes

Answer:

B. 0.813

Explanation:

A sixteen-sided number cube has the numbers 1 through 16 on each face.

So,
|\ S\ |=16

Let us assume that, A be the event that the number will be an even number. So,


A=\left \{ 2,4,6,8,10,12,14,16 \right \} and
|\ A\ |=8

Then,


P(A)=(|\ A\ |)/(|\ S\ |)=(8)/(16)

Let us assume that, B be the event that the number will be an odd prime number.


B=\left \{3,5,7,11,13 \right \} and
|\ B\ |=5

Then,


P(B)=(|\ B\ |)/(|\ S\ |)=(5)/(16)

So the probability that you will roll an even number or an odd prime number will be,


P(A\cup B)=P(A)+P(B)-P(A\cup B)


=(8)/(16)+(5)/(16)-0 ( as independent events)


=(13)/(16)


=0.813


User Gabriel Heming
by
8.4k points

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