Teri designed a game to play against her brother will in which teri flips a fair coin n times, and will wins if and only if exactly one of the flips lands heads up.
if there is a 25% chance of will winning the game, what is the value of n?

4

Step-by-step explanation:

Since the coin is fair, then the probability of each flip to be heads is 0.5. The number of heads obtained from flipping n coins is a random variable, that we will note X, with Binomial distribution B(n,0.5).

The probability of X being equal to 1 is

If n = 4, then PX(1) = 4 * 0.5⁴ = 0.25.

We can chech for small values:

The probability decreaces as long as n increase. So the only value of n for which the probability is 0.25 is n=4.