Question

A box contains cards number 1-10. A card is drawn at random, then replaced, and a second card is drawn. What is the probability that the first number is a multiple of 5 and the second number is prime?

Answer 1

Consider the pairs (a, b) where a represents the first draw, and b the second draw.

All cases where the 1st number is a multiple of 5, and the second number is a prime are:

{(5, 2), (5, 3), (5, 5), (5, 7), (10, 2), (10, 3), (10, 5), (10, 7),}

so we have in total 8 possible cases.

we could have found 8 also as follows:

2 possibilities for the first number {2, 5} combined with 4 possibilities for the second number {2, 3, 5, 7} makes 2*4=8.

similarly, we can find that there are 10*10=100 possible outcomes.


P(1.st multiple of 5, 2.nd prime)=8/100=0.08


Answer: 0.08