Question

You toss 3 coins. What is the probability that you get exactly 3 heads given that you get at least one head???

Answer 1

@ybarrap help quickly!!

Answer 2

@Luigi0210

Answer 3

is it 1/7??? please answer! I have to move on!

Answer 4

@Hero

Answer 5

your probability is 1 - 1/8 = 7/8

Answer 6

help

Answer 7

how do u know

Answer 8

@Jasmineflvs ????

Answer 9

here i got this from a person who asked the same exact question on openstudy
http://openstudy.com/study#/updates/4f85bd03e4b0505bf085c85a

Answer 10

the tree diagram shows it

Answer 11

its not the exact same question... :( :(

Answer 12

just a sec then

Answer 13

it is

Answer 14

if you need more help message a moderator or someone who has an experience in this

Answer 15

:( I had to submit it cuz i ran out of time :(

Answer 16

oh you had a time limit?

Answer 17

look at the tree (posted above) and find the number of "leaves" or paths that have at least one head. Count up the number.

Now count up the number in that set that have 3 heads (there is only 1 path with 3 heads)

the probability of 3 heads given 1 head is the ratio of those two numbers: 1/# of paths with at least 1 head

Answer 18

1/7

Answer 19

Probability of at least on head (given above, using tree in link) is 7/8
Probability of 3 heads and at least one head out of three is the same as probability of 3 heads, because this is the only way to match both conditions. This is 1/8

Probability of 3 heads given at least 1 head :

P(3 heads|at least 1 head)

\[= \frac{ P(3heads \cap at least 1 head) }{ P(at least 1 head) }\]
\[= \frac{ P(3heads) }{ P(at least 1 head) }\]
\[=\frac{ 1/8 }{ 7/8 }\]
\[=1/7\]