Two very easy statistics questions?

Question

I know these are very easy, but I'm not sure exactly how to calculate them.

1. What is the probability of having two boys and two girls (in any order) from four children?

2. What is the probability of having three boys and two girls (in any order) from five children?

If you could show me exactly how you got the probability that would be great.

Answer 1

1) P(boy)=0.5

P(girl)=0.5

P(2boys&2girls)=P(boy)P(boy)P(girl)P(g...

=0.5*0.5*0.5*0.5=0.0625

2)P(3boys&2girls)=P(boy)P(boy)P(boy)P(...

=0.5*0.5*0.5*0.5*0.5=0.03125

Notice that the probabilies don't change.  This is because having a boy and having a girl are independent events.  In other words, they don't depend of any result before.

I hope this can be useful.

David

Answer 2

4/4 and 5/5

Answer 3

1 in 5 is not the correct answer.

You have to list all the possible orders you could have the children...

B-B-B-B

B-B-B-G

B-B-G-G

B-B-G-B

B-G-B-B

B-G-B-G

B-G-G-G

B-G-G-B

G-G-G-G

G-G-G-B

G-G-B-G

G-G-B-B

G-B-G-G

G-B-B-B

G-B-G-B

G-B-B-G

So your answer is 6/16 or 3/8 or 37.5%

The same approach to the second problem should yield 31.25%

Answer 4

for both, list all possible outcomes. count them.

look for the desired outcome in the list. count them.

probability is desired divided by possible.

for #1.

possible out comes are

0-4

1-3

2-2

3-1

4-0

only 1 way to have 2-2 so prob is 1/5

i leave #2 to you.