two dice are rolled simultaneously what is the probability of getting fi 1=a prime number on each dice 2=a total of 9 or11
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Because you are summing the two dice, and the total numbers here are relatively small, a brute-force method is the easiest way.
N.b. computing this for, say, 421 dice to produce results divisible by 123 would be a very challenging question.
Two 6-sided dice are tossed. 6 x 6 = 36 so their are 36 distinct outcomes. As we are summing dice, we have possible sums of 2 - 12. Their frequency distributions are:
SUM, FREQUENCY
2, 1
3, 2
4, 3
5, 4
6, 5
7, 6
8, 5
9, 4
10, 3
11, 2
12, 1
So, there are 5 ways to roll a total of 6, 2 ways to roll an 11…
How many of these are divisible by 3 OR 4? 3, 4, 6, 8, and 12 of which there are 2, 3, 5, 5, and 1 respectively. Summing these, you get 16.
So the probability you throw a pair of dice and the result is divisible by 3 or 4 is 16/36 = 8/18 = 4/9.
N.b. computing this for, say, 421 dice to produce results divisible by 123 would be a very challenging question.
Two 6-sided dice are tossed. 6 x 6 = 36 so their are 36 distinct outcomes. As we are summing dice, we have possible sums of 2 - 12. Their frequency distributions are:
SUM, FREQUENCY
2, 1
3, 2
4, 3
5, 4
6, 5
7, 6
8, 5
9, 4
10, 3
11, 2
12, 1
So, there are 5 ways to roll a total of 6, 2 ways to roll an 11…
How many of these are divisible by 3 OR 4? 3, 4, 6, 8, and 12 of which there are 2, 3, 5, 5, and 1 respectively. Summing these, you get 16.
So the probability you throw a pair of dice and the result is divisible by 3 or 4 is 16/36 = 8/18 = 4/9.
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