IMPORTANT NOTE For these problems dont just give final resul

IMPORTANT NOTE: For these problems, don’t just give final result, show the steps (e.g. if using multiplication principle instead of saying “5040”, show what you multiply by what: 10*9*8*7. You can actually leave it as that, calculating what’s it equals to isoptional and just a technicality.)

A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes…

are there in total?

contain exactly three heads?

contain at least three heads?

contain the same number of heads and tails?

Solution

1.

2 possible outcomes on each toss and each toss is independent of the other so 2^8=256 outcomes total

2.

Choose 3 out of 8 tosses to be heads in

C(8,3)=8*7*6/6=56 ways

3.

a. Contains no heads =1 outcomes only with all tails

b. Contains 1 head= C(8,1)=8 outcomes

c. Contains 2 head=C(8,2)=8*7/2=28 outcomes

So outcomes with less than 3 heads are:1+8+28=37

So total outcomes with at least three heads =256-37=219 outcomes

Same number of heads and tails means 4 heads and 4 tails

So number of outcomes is:C(8,4)=8*7*6*5/4!=70