IB Mathematics Applications & Interpretation Question Type 4: Finding Expected Occurrences Using Probable Outcomes Exercises

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

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

When two fair coins are tossed, calculate the probability of obtaining 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 that no two heads occur consecutively.

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

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

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?

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

Four fair coins are tossed. Find the probability of obtaining exactly two heads.

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.