In a random number table, each digit is a random number from 0 to 9. In this set, the numbers 2, 3, 5, and 7 ...

In a random number table, each digit is a random number from 0 to 9. In this set, the numbers 2, 3, 5, and 7 are prime. Let X be the number of prime digits in randomly chosen block of 5 digits from a random number table. 

(a)  What is the probability that a single digit is prime?

(b)  Explain why X is binomially distributed, and find n and p such that its distribution is B(n, p).

(c)  Find P (X = 0), P (X = 1), . . . , P (X = 5). Sketch this probability distribution. Describe the shape of the distribution.