Question

What are the odds against getting exactly two heads in three successive flips of a coin?

The odds for are: 2/3

but I do not know how to figure out the probability of odds against getting exactly two heads in three successive flips.

Answer 1

"probability of odds" ? , no such thing

odds and probability are closely related

odds in favour of some event
= prob(event will happen) : prob(event will not happen)

so two heads in 3 flips could be
HHT
HTH
THH, which would be 3 cases out of the 8
prob of exactly two heads out of 3 = 3/5
prob of NOT exactly two heads out of 3 = 5/8

odds against exactly 2 heads out of 3 flips = 5:3

Answer 2

Suppose a coin is biased so that it has the probilities below for landing on heads or tails on a single toss of the coin.

P(h)=0.5020 P(t)=0.4980

If this coin is tossed twice find the probability P(hh)