probability problem

Question

Can you please help with this question?

Tiffany and Emily are playing a game of flipping coins. Tiffany says I bet when I flip three coins I will get at least 2 heads. Emily thinks not. What is the product of the probability Emily would be correct and Tiffany will be correct?

Answer 1

Jon could be right, but it seems to me like this might be a badly worded trick question.

you are going to toss 3 coins . Since the two girls Are selecting outcomes that Can NOT both occur, then the probability of tiffany being right And Emily being right is zero.

Or maybe you are supposed to think about both and notice that T and E are dependent (not independent) since you can’t just multiply the probabilities to get the probability of T and E

T= Tiffany Right

E=Emily Right

P(T and E) = 0

P(T) *P(E) = .5*.5 = .25.

.25 is Not the same as P(T and E) because if one Is right it changes the probability that the other is right.

Answer 2

Outcomes when tossing three coins:

HHH

TTT

HTT

THT

TTH

HHT

THH

HTH

4 out of 8 outcomes are at least 2 heads, so probability of getting at least 2 heads = 4/8 = 1/2

4 out of 8 outcomes are NOT at least 2 heads, so probability of NOT getting at least 2 heads = 4/8 = 1/2

Product of those probabilities = 1/4