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.
"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
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)
To calculate the odds against getting exactly two heads in three successive flips of a coin, we need to determine the number of unfavorable outcomes and divide it by the total number of possible outcomes.
First, let's determine the total number of possible outcomes. In three successive flips of a coin, each flip has two possible outcomes: either heads (H) or tails (T). As such, the total number of possible outcomes is 2 * 2 * 2 = 8.
Next, let's determine the number of unfavorable outcomes where exactly two heads appear. We can use combinations (nCr) to calculate this. In this case, we want to choose 2 positions out of 3 for the heads, as the remaining position will be a tail. Therefore, the number of unfavorable outcomes is given by the combination 3C2, which equals 3.
Finally, we can calculate the odds against getting exactly two heads by dividing the number of unfavorable outcomes by the total number of possible outcomes:
Odds against = Number of unfavorable outcomes / Total number of possible outcomes
Odds against = 3 / 8
So, the odds against getting exactly two heads in three successive flips of a coin is 3/8.