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If a dice is thrown 4 times, what is the probability that an odd numbe

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Bunuel
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If a dice is thrown 4 times, what is the probability that an odd numbe [#permalink] New post   16 Mar 2021, 03:00
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If a dice is thrown 4 times, what is the probability that an odd number will come up exactly 3 times ?

A. 1/2

B. 5/16

C. 1/4

D. 3/16

E. 1/8
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C
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Re: If a dice is thrown 4 times, what is the probability that an odd numbe [#permalink] New post   16 Mar 2021, 03:08
There are 3 odd numbers a d 3 even numbers out of the 6 numbers in a dice.

The probability of getting an odd number when a dice is thrown once is 1/2 and probability of getting a even number is the same 1/2.

Now the probability of getting exactly 3 odd numbers can be availed by arranging the probabilities of OOOE. This can be done by (4!/3!)*(1/2)^4

=4/2^4=1/4
Ans:C

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If a dice is thrown 4 times, what is the probability that an odd numbe [#permalink] New post   16 Mar 2021, 03:42
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Bunuel wrote:
If a dice is thrown 4 times, what is the probability that an odd number will come up exactly 3 times ?

A. 1/2

B. 5/16

C. 1/4

D. 3/16

E. 1/8



3 odd number and 1 even number:

Probability of an odd number = 3/6 = 1/2
Probability of an even number = 3/6 = 1/2

The position of the even number can be chosen in 4c1 = 4 ways

Probability = 4 x (1/2) x (1/2)³ = 4/16 = 1/4

Answer C

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Re: If a dice is thrown 4 times, what is the probability that an odd numbe [#permalink] New post   09 Oct 2022, 09:23
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Given that a dice is thrown 4 times and We need to find what is the probability that an odd number will come up exactly 3 times ?

As we are rolling a dice four times => Number of cases = \(6^4\) = 1296

Now lets pick the three times out of four when dice will land in an odd number. This can be done in 4C3 ways
=> \(\frac{4!}{3!*(4-3)!}\) = \(\frac{4*3!}{3!*1!}\) = 4 ways

Now, these three dice can get any of the three odd numbers (1, 3, 5) in 3*3*3 ways
The fourth dice can get any of the three even numbers (2, 4, 5) in 3 ways

=> Total number of cases = 4 * 3 * 3 * 3 * 3

=> Probability that an odd number will come up exactly 3 time = \(\frac{4 * 3 * 3 * 3 * 3}{6^4}\) = \(\frac{1}{4}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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Re: If a dice is thrown 4 times, what is the probability that an odd numbe [#permalink]
09 Oct 2022, 09:23
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