Calculating theoretical probabilities from two-way tables (two events) | Maths

Starter quiz

In a fair six-sided die, what is the probability of rolling a 5 and getting a head in a single toss of a fair coin?
- $\frac{1}{2}$
- $\frac{1}{6}$
- $\frac{1}{12}$ ✓
A counter is taken from the bag. Its letter is noted and then it is placed back into the bag. A counter is taken from the bag again. Which of these options is not the correct sample space?
- ξ = {AA, AB, AC, BA, BB, BC, CA, CB, CC}
- ξ = {AA, AB, BA, BB, BC, CA, CB, CC} ✓
If the probability of an event (A) is $/frac{3}{7}$ , and the experiment is repeated 49 times, what is the theoretical number of times event (A) will occur?
- 3
- 7
- 21 ✓
- 49
Which of the events {A,B,C} is the least likely to occur according to this probability tree?
- A ✓
- B
- C
- None.
John uses an unbiased random selection tool to generate a single letter of the alphabet. It is repeated three times. Which of the following letter sequences is the least likely?
- A,G,H
- A,A,A
- M,O,O
- B,I,N
- All selections are equally likely ✓
There are two trials. In Trial 1, a spinner with {A, B} is spun twice. In Trial 2, a spinner with {B, C} is spun twice. Which statement is true?
- The total number of possible outcomes in Trial 1 is greater than in Trial 2.
- The total number of possible outcomes in Trial 1 is less than in Trial 2.
- The total number of possible outcomes in Trial 1 is the same are in Trial 2. ✓

Exit quiz

If this spinner is spun twice, what is the probability that the sum of both results would be 11?
- $\frac{1}{32}$
- $\frac{1}{64}$
- $\frac{1}{16}$ ✓
- $\frac{11}{64}$
If this spinner is spun twice, what is the probability of not losing either time?
- $\frac{1}{9}$
- $\frac{1}{3}$
- $\frac{2}{9}$
- $\frac{4}{9}$ ✓
If this spinner is spun twice, what is the probability that the sum of both results would be odd?
- $\frac{1}{2}$ ✓
- $\frac{1}{4}$
- $\frac{1}{3}$
If spun twice what is the probability this spinner would spell 'pea' then 'nut' ?
- $\frac{1}{5}$
- $\frac{1}{25}$
- $\frac{2}{5}$
If each of these spinners is spun once, what is the probability of getting H and 6?
- $\frac{1}{10}$
- $\frac{1}{5}$
- 0 ✓
If this spinner is spun twice, what is the probability of the sum of the results being less than 10?
- $\frac{19}{64}$ ✓
- $\frac{23}{64}$
- $\frac{17}{64}$

Worksheet

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Lesson Details

Key learning points

The probability of an outcome can be found by considering a two-way table showing all possible outcomes for two events.
The probability of a set of outcomes can be found using a two-way table showing all possible outcomes for two events.
The probability of a set of outcomes can be found using a two-way table, even when the outcomes are not equally likely.

Common misconception

Pupils may struggle with finding the probability of A or B, and may count the outcomes that belong to A and B twice.

If you use an example, such as visiting particular countries, ask the pupils how someone would respond to the question 'have you visited X or Y' if they have in fact visited both countries.

Keywords

Theoretical probability - A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.