Stage 8 - Q1 - 2 marks
The probability of rain in a model is 0.35. Find the probability of no rain.
Hint
The two modelled outcomes are rain and no rain.
Stage 8 - Q2 - 2 marks
A game has winning probability \(\frac16\). Find the probability of not winning.
Hint
Write one as six sixths.
Stage 8 - Q3 - 2 marks
A box has 9 green and 15 purple buttons. One is chosen at random. Find the probability it is not purple.
Hint
Count the whole collection.
Stage 8 - Q4 - 2 marks
There are 8 circles, 11 triangles and 5 squares in a bag. Find the probability of selecting a shape that is not a triangle.
Hint
The complement can contain more than one category.
Stage 8 - Q5 - 3 marks
A spinner lands on gold with probability \(\frac38\). In a model of 64 equally likely positions, how many positions are not gold?
Hint
Find a fraction of sixty-four.
Stage 8 - Q6 - 3 marks
A spinner has only red, blue and yellow. Red has probability 0.27 and blue has probability 0.31. Find the probability of not yellow.
Hint
You can find the complement directly without first calculating yellow.
Stage 8 - Q7 - 4 marks
A die has faces 1 to 6. A pupil says “not greater than 4” means “less than 4”. Explain the error and find the correct probability for a fair die.
Hint
Test the statement with a score of exactly four.
Stage 8 - Q8 - 4 marks
Design a bag with 30 counters in three colours. The probability of not red must be \(\frac35\), and blue and green counts must be equal. Give all three counts.
Hint
Use the complement to fix the red count first.
Stage 8 - Q9 - 5 marks
A spinner has only red, blue and green. \(P(\text{not red})=0.72\) and \(P(\text{not blue})=0.61\). Find green. Why does adding the two given probabilities double-count something?
Hint
Write the colours included in each complement.
Stage 8 - Q10 - 6 marks
A bag has only red and blue counters. Initially \(P(\text{not red})=\frac35\). After ten red counters are added, \(P(\text{not red})=\frac12\). Find the original counts.
Hint
The complement is blue before and after the change.