Question

Suppose I roll a six-sided die and then flip a coin and record the results. How many ways can I get an even number with heads or a prime number with tails? (Note: technically speaking, 1 is not prime.)

Answer 1

Answer: 6

Step-by-step explanation

H = heads, T = tails

Something like H2 means "flipped heads and rolled a 2".

The subset {H2,H4,H6} is when we flipped heads and rolled an even number.

The subset {T2,T3,T5} is when we get tails and a rolled a prime number.

Glue those two sets together, i.e. do a set union, and we get this event space.

{H2,H4,H6, T2,T3,T5}

There are 6 ways to get an even number with heads or a prime number with tails.

Side notes:

• The event space is the set of things we want to happen.
• The sample space is the set of all possible outcomes.
• There are 2*6 = 12 items in the sample space.