what are the odds in favor of getting at least one head in three successive flips of a coin?
I need to know the formula on this. I have 1/6 over 1- 1/6. But I can't figure out how to do the math. Am I right?
the probability of getting at least one head is = 1-prob(three tails)=1-1/8=7/8
so the odds are 7:1 to get at least one head.
It' is the other way around if you multiplt your runner.
To calculate the odds in favor of getting at least one head in three successive flips of a coin, you can use the following formula:
P(at least one head) = 1 - P(no heads)
To calculate P(no heads), you need to calculate the probability of getting tails in all three flips of the coin, since getting no heads means getting all tails.
The probability of getting tails in a single flip of a fair coin is 1/2. Since you want to find the probability of getting tails in all three flips, you can multiply the probabilities of each flip:
P(no heads) = (1/2) * (1/2) * (1/2) = 1/8
Now, you can calculate the probability of getting at least one head as:
P(at least one head) = 1 - P(no heads)
= 1 - 1/8
= 7/8
Therefore, the odds in favor of getting at least one head in three successive flips of a coin is 7/8.
Regarding your initial attempt, it seems there was a mistake in the calculation. You mentioned 1/6, which is not the correct probability for getting a head in a single flip. The correct odds can be found using the approach explained above.