Question Type 4: Finding expected occurrences using probable outcomes Exercises

Find the probability of exactly one head when two fair coins are tossed.

Two fair coins are tossed once each. What is the probability of no heads?

When two fair coins are tossed, what is the probability of at least one head?

Three fair coins are tossed. Calculate the probability of at least one head.

Three fair coins are tossed. Find the probability of exactly two tails.

A fair coin is tossed four times. Find the probability that exactly one head appears in the first two tosses AND exactly one tail appears in the last two tosses.

Two fair coins are tossed. Given that at least one head appears, what is the probability that both are heads?

Two fair coins are tossed. Given exactly one head appears, what is the probability that the first toss is a head?

Four fair coins are tossed. What is the probability of exactly two heads?

Three fair coins are tossed. What is the probability that heads and tails alternate (no two identical outcomes adjacent)?

Three fair coins are tossed. Find the probability that no two heads occur consecutively.

For $n$ independent fair coin tosses, derive the probability of getting exactly $k$ heads.