Your little brother just learned how to flip and catch a coin. he believes that by catching the coin in mid-air, he can influence the probability that it will land heads up. based on your understanding of theoretical probability, explain to your little brother why his theory of influence is false.

If a coin is fair then it has two faces , one is heads and the another is tails.

The probability getting any favorable outcomes is given by the formula :-

So the factor effecting probability is just the number of  favorable outcomes and total outcomes.

If a coin is tossed then the probability of getting heads will be :-

To get heads always this should be 1 , which can be happen if number of  favorable outcomes is equal to total outcomes.

i.e. Number of heads = Number of total outcomes, this means coin should be biased.

Catching the coin in mid-air can never be a factor for this.

Therefore, the little brother's theory is false.

b is the correct answer