Question

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

Answer 1

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

Answer 2

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`