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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

Respuesta :

texaschic101
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
InesWalston

Answer:

B. 0.813

Step-by-step explanation:

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

So, [tex]|\ S\ |=16[/tex]

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

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

Then,

[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]

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

[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]

Then,

[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]

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

[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)

[tex]=\dfrac{13}{16}[/tex]

[tex]=0.813[/tex]


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