Question

A box contains 3 different coins. An experiment consists of drawing two coins in succession without replacement from the box, noting the type of each coin as it is drawn, and then flipping the last coin drawn 4 times and noting the number of Heads. An outcome is a list of the coins drawn, in the order they were drawn, and the number of Heads that came up on the 4 flips. How large is the sample space?

Answer 1

First coin can be taken out in : 3 ways

Second coin can be taken out in: 2 ways

For the 3rd coin, if we toss it 4 times, we can get either 0H or 1H or....4H. However total no of outcomes will be 2⁴ = 16 but we are interested only in no of H so no of outcomes: 5

So, no of elements on the sample space = 3•2•5 = 30