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Practice — Probabillity and Statistics • Probability

Probability with one coin

A fair coin is tossed once. What is the probability of getting heads?

Your Answer:

\(\dfrac{1}{2}\)

\(\dfrac{1}{3}\)

\(\dfrac{2}{3}\)

\(1\)

Solution:

A fair coin has 2 equally likely outcomes: heads or tails.
There is 1 favourable outcome for heads.
So the probability is \(\dfrac{1}{2}\).

Probability with two coins

Two fair coins are tossed. What is the probability of getting two heads?

Your Answer:

\(\dfrac{1}{2}\)

\(\dfrac{1}{4}\)

\(\dfrac{3}{4}\)

\(\dfrac{1}{8}\)

Solution:

The possible outcomes are HH, HT, TH and TT.
There are 4 equally likely outcomes.
Only 1 outcome gives two heads.
So the probability is \(\dfrac{1}{4}\).

Exactly one head

Two fair coins are tossed. What is the probability of getting exactly one head?

Your Answer:

\(\dfrac{1}{4}\)

\(\dfrac{1}{2}\)

\(\dfrac{3}{4}\)

\(\dfrac{1}{8}\)

Solution:

The possible outcomes are HH, HT, TH and TT.
Exactly one head happens in HT and TH.
That is 2 outcomes out of 4.
So the probability is \(\dfrac{2}{4}=\dfrac{1}{2}\).

No heads in three tosses

A fair coin is tossed three times. What is the probability of getting no heads?

Your Answer:

\(\dfrac{1}{8}\)

\(\dfrac{1}{4}\)

\(\dfrac{3}{8}\)

\(\dfrac{1}{2}\)

Solution:

No heads means all three tosses are tails.
The only successful outcome is TTT.
There are \(2^3=8\) equally likely outcomes in total.
So the probability is \(\dfrac{1}{8}\).

At least one head

A fair coin is tossed three times. What is the probability of getting at least one head?

Your Answer:

\(\dfrac{1}{8}\)

\(\dfrac{3}{8}\)

\(\dfrac{7}{8}\)

\(\dfrac{1}{2}\)

Solution:

There are \(2^3=8\) equally likely outcomes.
The only outcome with no heads is TTT, so \(P(\text{no heads})=\dfrac{1}{8}\).
Therefore \(P(\text{at least one head})=1-\dfrac{1}{8}=\dfrac{7}{8}\).