a fair number cube is rolled twice what is the probability that the first roll is prime and the second roll is composite

Question

 ​a fair number is rolled twice, What is the prabability that the first roll is prime and the second roll is composite

Answer 1

If the primes between 1 and 6 are: 1, 2, 3, 5 then the composites are 4 and 6. The chances of rolling a prime are 4/6=2/3 and of rolling a composite are 2/6=1/3. So the combined probability is 2/3*1/3=2/9.

If 1 is neither a prime nor a composite, the combined probability changes to 3/6*2/6=1/2*1/3=1/6.

Answer 2

First of all you need to know what numbers are the prime numbers. For numbers 1-6, the prime numbers are 2,3 and 5. So you have 3 prime numbers with a total outcome of 6 so the probability that the first roll is a prime number is 1/2.

Rolling a die is an independent event, which means that rolling the second time doesnt depend on the first roll etc. For numbers 1-6, only 4 and 6 are composite numbers which means that you have a probability of getting a composite number of 2/6 or 1/3.

If you were asking for the probability of first getting a prime number AND THEN getting a composite number on the second roll then just multiply both events together: 1/2 * 1/3 = 1/6

So theres a 1/6 probability of getting a prime number on the first roll and then a composite number on the second roll.

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