Algebra 2 Probability Problem?

Question

Ive been trying forever and I cant get the answer. If anyone knows how to work this out, please feel free to help out. Also, Please explain how you did it so can understand how to do it. Thanks!

If Jack and Jill each flip a coin three times, what is the probability they will get the same number of heads?

????????????

Answer 1

5/16, or about 31%.

Probability that they will both get 0 heads:
1/8 *1/8 = 1/64

Probability that they will both get 1 head:
3/8 * 3/8 = 9/64

Probability that they will both get 2 heads:
3/8 * 3/8 = 9/64

Probability that they will both get 3 heads:
1/8 * 1/8 = 1/64

1 + 9 + 9 + 1 = 20

20/64 = 5/16

Answer 2

There are 8 possible outcomes for the three coin tosses.

TTT, TTH, THT, HTT, THH, HTH, HHT, HHH.

The easiest way in such a limited run is to look at each number of heads results separately:

3 heads: 1/8. Odds that both flip 3 heads: (1/8)^2 = 1/64.
2 heads: 3/8. Odds that both flip 2 heads: (3/8)^2 = 9/64.
1 heads: 3/8. Odds that both flip 1 heads: (3/8)^2 = 9/64.
0 heads: 1/8. Odds that both flip 0 heads: (1/8)^2 = 1/64.

The odds that they will flip the same number of heads is simply the sum of these: 20/64 = 5/16.

Generalizing this to any number of coin tosses is probably beyond the scope of an algebra 2 class. (It involves summation and factorals. If this is in line with the material covered in the class, post an edit to your message and I'll give a more thorough answer.)

Answer 3

OK

Jack flips - he has 8 possibilities
HHH ,HHT, HTH, HTT, THH, THT, TTH, TTT
3,2,2,1,2,1,1,0
so Jack has
1/8 to get 3 heads
3/8 to get 2 heads
3/8 to get 1 head
1/8 to get 0 heads

Jill does the same. Same 8 possibilities. Same 4 probabllity outcomes.

Here is where it gets a little tricky. If Jack gets 3 or 0 heads, Jill has a 1/8 chance of matching him. Conversely, if Jack gets 2 or 1 head, Jill has a 3/8 chance of matching.

So :
1/8 chance and 1/8 to match = 1/64
3/8 chance and 3/8 to match = 9/64
3/8 chance and 3/8 to match = 9/64
1/8 chance and 1/8 to match = 1/64

So the chances of matching are 20/64 or 5/16 = 31.25% chance they will match.

Hope that helps.