probability

Question

Can I get some help with answering the below questions using the counting principle?

1. A coin is tossed three times. What is the probability of getting heads just once?

2. A month is chosen at random, then a standard die is rolled. What is the probability of getting February, then a number less than 5?

Answer 1

1.  A coin is flipped three times.  For heads to show up just once, it must be on either the first, second, or third flip.  So there are three possibilities.  For each flip there are two possible outcomes (heads or tails), so 2x2x2 = 8, meaning there are 8 possible outcomes total.  So the probability of getting heads just once is 3/8.

 

2.  The probability of choosing February is 1/12.  Since there are four numbers less than five on a die, and six numbers total, the probability is 4/6.  Now just multiply them together and you get (1/12)(4/6) = 4/72 = 1/18.

Answer 2

1.  P(htt)+ p(tht) + p(tth) = 1/8 + 1/8+1/8 = 3/8.

 

2.  p(f)* P(die<5) = 1/12 * 4/6 = 1/18.