If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
Solution:
Given a fair die is rolled three times.
A fair die has 6 faces, hence, the sample space will be {1, 2, 3, 4, 5, 6}
So, on rolling a die thrice, the number of elements in sample space is 63 = 216
Let us assume that the die in the first roll shows 3, hence the second die and third die can show any of the other 5 numbers.
First, the probability of rolling a single value (in this case 3) on a fair 6-sided die would be one out of six.
The probability of NOT rolling that number would be five out of six.
Let P be the probability of getting 3 only once
P= 1/ 6 × 5/6 × 5/6 = 25/216
The number 3 can be showed in any of the three dies at a time
Hence required probability = 25/216 + 25/216 + 25/216 = 75/216 = 25/72
P = 25/72
Therefore, the probability that exactly one 3 is rolled is 25/72.
If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled?
Summary:
If a fair 6-sided die is rolled three times, then the probability that exactly one 3 is rolled is 25/72.
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