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If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one

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If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one

by BTGmoderatorDC » Tue Mar 01, 2022 8:06 pm

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If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number?

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8


OA D

Source: Princeton Review
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Re: If a six sided die is rolled three times, what is the probability of getting at least one even number and at least o

by regor60 » Fri Mar 18, 2022 4:18 am
BTGmoderatorDC wrote: ↑
Tue Mar 01, 2022 8:06 pm
 If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number?

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8


OA D

Source: Princeton Review
Satisfying the requirement would mean the following possible outcomes without regard to order:

OOE OR EEO

Either one of the above in its 3 permutations would satisfy.

Because EITHER one would work, their probabilities are added, but there's an easier way.

The only other possible outcomes are

EEE or OOO.

We can subtract the probabilities of these two from 1 to arrive at the answer;

3 even numbers and 3 odd on each side, so probability of either is 1/2. Probability of 3 in a row is then

1/2*1/2*1/2 = 1/8. Since there are 2 ways, multiply by 2 =

1/4.

Subtract from 1= [spoiler]3/4,D[/spoiler]
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