probability · Year 6 · Suggested learning sequence
Two events and complements
An event and its complement (the event not happening) always add up to 1. If P(rain) = 3/10, then P(no rain) = 1 − 3/10 = 7/10. For two separate events, such as tossing a coin and rolling a dice, draw a table: 2 × 6 = 12 equally likely outcomes. Count the cells where both happen. 'Not both' is every other cell, so take the 'both' cells away from all the cells.
Sample questions
A bag has 6 counters. The probability that you take a red counter is 5/6. What is the probability that you do NOT take a red counter?
- An event and its complement (the event not happening) always add up to 1.
- 1 = 6/6, so take away 5/6: 6/6 − 5/6 = 1/6.
- P(not) = 1/6.
Answer: 1/6
A bag has 9 counters. The probability that you take a red counter is 7/9. What is the probability that you do NOT take a red counter?
- An event and its complement (the event not happening) always add up to 1.
- 1 = 9/9, so take away 7/9: 9/9 − 7/9 = 2/9.
- P(not) = 2/9.
Answer: 2/9
The probability that it rains tomorrow is 6/10. What is the probability that it does NOT rain tomorrow?
- An event and its complement (the event not happening) always add up to 1.
- 1 = 10/10, so take away 6/10: 10/10 − 6/10 = 4/10.
- P(not) = 4/10 = 2/5.
Answer: 2/5