23.1 The probability scale and equally likely outcomes — Practise

1. A probability is $0.7$. Is the event more likely or less likely than not?

Answer: More likely than not, because $0.7>0.5$.

2. A fair six-sided die is rolled. Find the probability of a prime number.

Answer: $\frac{3}{6}=\frac12$.

3. A spinner has 3 blue and 5 yellow equal sectors. Find the probability it does not land on blue.

Answer: $1-\frac38=\frac58$.

4. A fair die is rolled. Find the probability of a result from 1 to 6.

Answer: $1$; the event is certain.

5. Two fair dice are rolled. Find the probability their total is 7.

Answer: Six of 36 outcomes total 7, so $\frac16$.

6. The probability a bus is late is $0.18$. Find the probability it is not late.

Answer: $1-0.18=0.82$.

7. Write $\frac{3}{5}$ as a percentage.

Answer: $60\%$.

8. A bag has 7 red, 2 green and 1 blue counter. Find the probability of green.

Answer: $\frac{2}{10}=\frac15$.

9. A fair coin is tossed. Find the probability it lands on both heads and tails at once.

Answer: $0$; the event is impossible.

10. A bag has 4 white and 6 black counters. Find the probability of not choosing white.

Answer: $1-\frac4{10}=\frac35$.

11. A fair six-sided die is rolled 60 times. Find the expected number of fives and the expected relative frequency of fives.

Answer: The expected number is $60\times\frac16=10$. The expected relative frequency is $\frac{10}{60}=\frac16$, the theoretical probability.