Statistics & Probability · Guided Practice
Probability and Risk
11 questions with answers and video solutions. Try each one before revealing the answer.
One counter is taken at random.
Calculate the probability that it is red.
Answer
Calculate the probability of scoring more than .
Answer
Two pens are taken at random without replacement.
Calculate the probability that both are red.
Answer
A company runs trains in a month.
Calculate the expected number of late trains.
Answer
Three trains run independently.
Calculate the probability that all three arrive on time.
Answer
Machine A failed times in runs.
Machine B failed times in runs.
Determine which machine is more reliable. Use your working to justify your answer.
Answer
Machine B: failure rate
Machine A is more reliable, as its failure rate is lower.
Michael runs a stall at the school fayre.
His game requires two spinners to be spun and allowed to come to rest.
The spinners are shown below.
The numbers on which the spinners come to rest are multiplied together.
To win a prize the answer to this multiplication must be less than 5.
Calculate the probability of winning a prize.
Answer
Jade runs a game stall at the Christmas coffee morning.
Her game requires two spinners to be spun and allowed to come to rest.
The spinners are fair and are shown below.
The numbers on which the spinners come to rest are multiplied together.
To win a prize the answer to this multiplication must be greater than 30.
Calculate the probability of winning a prize.
Answer
Eddie runs a stall at the school fundraiser.
His game requires two spinners to be spun and allowed to come to rest. The spinners are shown.
A prize is won if one spinner lands on blue or green and the other spinner lands on an even number.
Calculate the probability of NOT winning a prize.
Answer
A lottery consists of a draw with 49 balls numbered from 1 to 49.
In the draw six numbered balls are drawn and not replaced.
These six numbers were 3, 7, 12, 13, 28 and 42.
A further bonus ball is then drawn.
Calculate the probability of the bonus ball being a number less than 8.
Answer
Balls remaining = 43
Numbers less than 8 remaining (1, 2, 4, 5, 6) = 5 balls
Probability =
Lesley ran a game stall at her local gala.
The game requires two spinners to be spun and allowed to come to rest.
The spinners are fair and are shown below.
To win a prize, spinner B must land on a larger number than spinner A.
(a) Calculate the probability of winning a prize.
Answer
(or , 25%, 0.25)