What are the odds in favor of getting at least one head

in three successive flips of a coin?

1/2 * 1/2 * 1/2

ooops, I misread. One head in three tries, so there are three ways

HTT
THT
TTH

So it is 3*1/2*1/2*1/2

The prob of at least one head with 3 coins

= 1 - 1/8
= 7/8
(I excluded the case of all tails)

so the odds in favour of at least one head
= (7/8):(1/8)
= 7:1

To determine the odds in favor of getting at least one head in three successive flips of a coin, we need to find the probability of this event occurring.

First, let's calculate the probability of getting at least one head in a single coin flip. The coin has two possible outcomes - either heads or tails. Since we want to calculate the probability of getting at least one head, we need to subtract the probability of getting all tails from the total probability.

The probability of getting all tails in a single flip is 1/2 (since there are two possible outcomes, and getting tails is only one of them).

Therefore, the probability of getting at least one head in a single flip is 1 - 1/2 = 1/2.

Now, to calculate the probability of getting at least one head in three successive flips, we can use the concept of complementary probability. The complementary probability is the probability of the event not occurring.

In this case, the complementary event is getting all tails in three flips. The probability of getting all tails in a single flip is 1/2, so the probability of getting all tails in three flips is (1/2)^3 = 1/8.

Therefore, the probability of getting at least one head in three flips is 1 - 1/8 = 7/8.

Now, let's talk about odds. Odds are generally expressed as a ratio of favorable outcomes to unfavorable outcomes. In this case, the odds in favor of getting at least one head would be 7 favorable outcomes (getting at least one head) to 1 unfavorable outcome (getting all tails).

So, the odds in favor of getting at least one head in three successive flips of a coin are 7 to 1.