Question

A coin is flipped 8 times. What is the probability that both heads and tails occur?

Answer 1

Answer:

Given,

To determine the probability that both heads & tails occur

A coin is flipped 8 times

The probability is 1 less the probability of getting all heads or getting all tails.

On the off chance that you don't get all heads or all tails you should have at any rate one of each.

The probability, with a reasonable coin, of getting any one explicit succession is 1 separated by 2 to the intensity of the length of the arrangement.

So the probability of 8 all heads is 1 partitioned by (2^8), or 1/256.

The probability of 8 all tails is 1 partitioned by (2^8), or 1/256.

Since we said 'or' above, we can include these two together

i.e.,

= 1/256 + 1/256

= 2/256

= 1/128

to give a probability of 1/128 for getting either all heads or all tails.

That leaves a probability of 1 - 1/128, or 127/128 as the probability of getting the two heads and tails when flipping a reasonable coin 8 times.