Three dice are rolled simultaneously. What is the probability that all three will show a 4?
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Answer:
Step-by-step explanation:
The dice will show different numbers twice if either in one throw they show the same number or any two of them show the same number and in two throws they all show different numbers.
In one throw they show the same number and in two throws they all show different numbers:
1
3
C∗{(
6
1
)∗(1)∗(1)}∗{(1)∗(
6
5
)∗(
6
4
)}
2
=
162
25
In one throw any two of them show the same number and in two throws they all show different numbers:
1
3
C∗{
2
3
C∗(
6
1
)∗(1)∗(
6
5
)}∗{(1)∗(
6
5
)∗(
6
4
)}
2
=
324
125
Hence, the required probability =
162
25
+
324
125
=
324
175
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