Beth spins a fair spinner numbered 1 - 8 and flips a fair coin.

What is the probability of obtaining a factor of 3 and a head?

1/8

Step-by-step explanation:

To find the probability of two events happening we need to find the probability of each event happening first:

For the spinner there are 8 possibilites (landing 1, 2, 3 ... 8) and we are looking for factors of 3 which are 1 and 3 (3 is prime) therefore:

The chance of landing a factor of 3 on the spinner is 2/8=1/4

For the head there are two possibilities (heads and tails) and only one event we want happening (heads), therefore:

The chance of landing on heads on a fair coin is 1/2

Now to find the chances of both events happening we must multiply them to find that:

(1/2) ⋅ (1/4) = 1/8 the chances of the event happening