Question

A box contains 3 plain pencils and 5 pens. A second box contains 6 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?

Answer 1

P(a pen from the first box) = 5/(3+5) = 5/8

P(a crayon from the second box ) = 2/(6+2)=2/8=1/4

P(a pen from the first box AND a crayon from the second box) =5/8*1/4 =5/32

Answer : 5/32. 

Answer 2

Prob(a pen chosen from first box) = 5/8

Prob(crayon chosen from second box) = 2/8

Required probability = 5/8 * 2/8 = 10/64  = 5/32 (answer).

The 2 probabilities are multiplied because the 2 events are independent of each other.