Question

A coin is tossed three times. What is the probability that there is at least one head and at least one tail?

Answer 1

there are 8 equally likely possibilities when you toss 3 coins
8 is not such a large number that we cannot list them all

Answer 2

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT

Answer 3

I know there are 8 possibilities so the answer would be 6/8, but how to you get that by using the multiplication or addition rule?

Answer 4

@satellite73

Answer 5

count

Answer 6

HHT HTH THH HTT THT TTH have at least on head and at least one tail

Answer 7

@satellite73 I need to use one of the probability rules as proof though. I'm thinking its the multiplication rule but am stuck at this point

Answer 8

i think counting is best, not sure why you have to use some "rule"
i suppose you could say "at least one head and at least one tail" is the same as "not all heads or all tails" and compute \[1-\frac{1}{8}-\frac{1}{8}\] but that seems like donkey work to me

Answer 9

ah okay yeah that helps. Yeah I feel the same but that is how the problem is worded so better to just follow directions. Thanks!