Single events. A fair die is rolled once. Find \(P(\text{even})\).

1. \(\dfrac{1}{2}\)
2. \(\dfrac{1}{3}\)
3. \(\dfrac{2}{3}\)
4. \(\dfrac{1}{6}\)

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

The even numbers on a die are 2, 4 and 6 - three favourable outcomes.

\(P = \dfrac{3}{6}\)

Single events. A fair die is rolled once. Find \(P(\text{not } 6)\).

1. \(\dfrac{5}{6}\)
2. \(\dfrac{1}{6}\)
3. \(\dfrac{1}{2}\)
4. \(\dfrac{2}{3}\)

Answer: \(\dfrac{5}{6}\)

Use the complement: \(P(\text{not } 6) = 1 - P(6)\)

\(= 1 - \dfrac{1}{6}\)

Tip: Subtracting from 1 is quicker than counting the five other faces.

Single events. Which of these can NOT be a probability?

1. \(1{,}2\)
2. \(0{,}75\)
3. \(\dfrac{3}{8}\)
4. \(0\)

Answer: \(1{,}2\)

Every probability satisfies \(0 \leq P \leq 1\).

\(1{,}2\) is greater than 1, so it is impossible.

Tip: An answer outside 0 to 1 always means an arithmetic slip.

Single events. A fair die is rolled. Find \(P(\text{a prime number})\).

1. \(\dfrac{1}{2}\)
2. \(\dfrac{1}{3}\)
3. \(\dfrac{2}{3}\)
4. \(\dfrac{5}{6}\)

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

The primes on a die are 2, 3 and 5. (1 is not prime - it has only one factor.)

\(P = \dfrac{3}{6}\)

Relative frequency. A coin is tossed 600 times and lands heads 312 times. What is the relative frequency of heads?

1. \(0{,}52\)
2. \(0{,}5\)
3. \(0{,}48\)
4. \(1{,}92\)

Answer: \(0{,}52\)

relative frequency \(= \dfrac{\text{times it happened}}{\text{number of trials}}\)

\(\dfrac{312}{600} = 0{,}52\)