Answer:
A 3/8
Explanation:
2 digits with 9 options (as there is no 0).
and no double digits allowed.
that gives us 9 options for the first and then only 8 options for the second digit (as whatever was picked for the first, cannot be picked again for the second position).
in total
9×8 = 72
possible combinations.
and we are looking for the probability that the second digit is a prime number, when the first digit was already a prime number.
P(B|A) = P(B and A)/P(A)
we need prime numbers. what prime numbers are possible ?
2, 3, 5, 7
that means we have 4 desired cases out of 9 for theoretically each position (4/9), but again one less for the second position : 3 out of 8 (3/8).
that gives us as combined probability of A and B
4/9 × 3/8 = 12/72
the probability that the first digit is a prime number is again 4/9.
so, formally, we have for
P(B|A) = 12/72 / 4/9 = 12×9 / 4×72 = 12 / 4×8 =
= 3/8