Question

you flip three coins. what is the probability that you get at least two tails, given that you get at least one tail?

Answer 1

given you have at least one tail cuts down the sample space, and gets rid of the even that you get (h, h, h) so you have 7 elements in the sample space, rather than the usual 8

Answer 2

total sample space is now
(h, h , t)
(h, t, h)
(t, h, t)
(h, t, t)
(t, h, t)
(t, t, h)
(t, t, t)

of those you can count how many have at least two tails

Answer 3

sorry i meant "gets rid of the EVENT that you get 3 heads"

Answer 4

i still don't get it...

Answer 5

ok lets go slow

Answer 6

the line that reads
" given that you get at least one tail?" means you know for sure you have tossed at least one tail in the three tosses

Answer 7

i got that

Answer 8

when you flip 3 coins, since there are two possible outcomes for each coin (H or T) you know by the counting principle that there are \(2\times 2\times 2=2^3=8\) possible outcomes
since 8 is not such a big number, we can list all of them

Answer 9

(h, h, h)
(h, h , t)
(h, t, h)
(t, h, t)
(h, t, t)
(t, h, t)
(t, t, h)
(t, t, t)

there are the 8 possibilities for tossing 3 coins

Answer 10

of those 8, since you are told you have at least one tail, we can get rid of the first one, since that one has not tails

Answer 11

*no tails

Answer 12

okay

Answer 13

that leaves 7 possible outcomes, not 8

Answer 14

now you want to count, out of those 7, how many have "at least 2 tails"

Answer 15

5?

Answer 16

i count exactly 4, namely
(h, t, t)
(t, h, t)
(h, t, t) and
(t, t, t)

Answer 17

oh yea ok 4

Answer 18

those have "at least two tails"

Answer 19

so the answer is four out of seven, i.e. \(\frac{4}{7}\)

Answer 20

okay thanks!

Answer 21

yw