Probability Revision

Question 1

a)Draw and complete the Likelihood Scale

b)Probability is always between …………………….

c)The sum of probabilities add up to…….
Give an example

Question 2

Calculate the probability of the following events A, B, C, D, E and F. Place the letter at its most appropriate position on the probability scale below.

  1. You roll a fair dice and score a 2. Probability =
  2. Your birthday is on Feb 30th. Probability =
  1. Your choose a green marble from a bag containing 2 blue marbles, 2 red marbles and 6 green marbles. Probability =
  1. You choose a green or a blue or a red marble from a jar containing green, blue and red marbles. Probability =
  1. You choose an even number from the numbers between 1 and 10. Probability =
  1. You choose a prime number from the numbers between 1 and 20. Probability =

Question 3

Paul has some boxes containing different coloured counters:
Box A has 8 blue counters

Box B has 1 blue and 5 yellow counters

Box C has 3 red, 1 blue and 2 yellow counters

Paul takes one counter from each box without looking.

a)There is a 50:50 chance that Paul picks a red counter from which box? Explain your answer.

b)What is the probability that Paul picks a green counter from these boxes?

c)It is more likely that a yellow counter will be chosen from which box? Explain your answer.

d)It is impossible to pick a yellow counter from which box? Why?

e)What changes could be made to the counters in Box C so that there is an even chance that Paul will pick a yellow counter?

f)How many red counters could be put into Box A so that it would be more likely that Paul would choose a red than a blue counter? Is the answer just one number? Explain your answer.

g)There are only two colours in Box B. Eva says that because there are only two colours in Box B that Paul is just as likely to choose a yellow as a blue. Is she correct? Explain your answer.

Question 4

a)A coin is tossed 500 times with the following outcomes.

Heads / Tails
210 / 290
  1. What is the relative frequency of heads occurring? Give your answer as a fraction and a decimal.

Colour / Red / Blue / Yellow / Green
Relative / 0.23 / 0.12 / 0.4
  1. What is a probability of head occurring? Give your answer as a fraction and a decimal.
  1. Would you say is the coin biased?

b)A spinner has four sectors: red, blue, yellow and green. The spinner is spun a number of times and the relative frequencies are recorded below:

  1. Calculate the relative frequency of green occurring.
  1. Calculate the relative frequency of a blue or red occurring.

c)A tennis player analysing her serve finds that she missed 18 of her last 50 first serves.

  1. What percentage of her first serves were in?
  1. What is the relative frequency of her first serve being in?

d)A group of children are playing a game of ‘crossbar challenge’, where they take a shot and try to hit the crossbar. The winner is the first to reach 6. Jessica hits the crossbar with 2 out of her first 10 shots.

  1. What is the relative frequency of Jessica hitting the crossbar?
  1. Jessica won the game. How many shots would you expect her to have taken?

e)A baby throws a piece of buttered toast in the air 20 times. It lands on the buttered side down 12 times. What is the relative frequency of the toast landing buttered side up?