Numeracy at Key Stage 3

Single Event Probability

When calculating single event probability:

  • First find all possible outcomes that fit the description
  • Count how many outcomes there are
  • Write it as a probability
  • Simplify your answer whenever possible

For example, to solve question 1:

  • All possible odd outcomes: 1,3,5,7
  • That makes 4 outcomes
  • So 4/8
  • Simplify it to ½

1. There are 8 counters in a box numbered 1, 2, 3, 4, 5, 6, 7 and 8. If one counter is drawn out at random, what is the probability that it is a counter:-

a) with an odd number,       b) with an even number,

c) with a square number,       d) that is greater than or equal to 6?

2. I have a pack of playing cards, containing 52 cards. I pick a card at random. What is the probability that the card I select is:-

a) a king,       b) a diamond,

c) a black card,       d) the jack of clubs?

3. There are four different coloured writing pads. In a pack there are three blue, eight red, one white and four green. What is the probability when I open a new pack I randomly pick a :-

a). blue pad,       b) red pad,        c) white pad,
d) green pad,       e) yellow pad,       f) red or green pad?

4. Draw the number line in your book. The number line represents all possibilities. Indicate, by arrows labelled "a" to "f" the probabilities for :-

a) throwing a tail on a coin,      b) cutting a diamond from a pack of a cards,

c) saturday following friday,      d) the water being cut off today,

e) scoring a 2 or a 3 on a dice,      f) your teacher becoming a dinosaur.

5. Arrange these events in order of which is “most likely" down to which is "least likely":-

a) throwing a dice and getting a "1".       b) being born on a day with "y" in it.

c) spinning a coin and it landing on a tail.       d) somebody having their birthday on New Year's Day.

6. Arrange these events in order of which is "most likely" down to which is "least likely":-

a) picking a red card from a pack of cards.       b) a fair 4 sided spinner labelled 1, 2, 3, and 4 landing on 4.

c) eating a meal some time this month.       d) winning the jackpot of the National Lottery.

7. A biased coin has a probability of landing on heads of 0.6. What is the probability of landing  on tails?

8. Another biased coin has a probability of landing on tails of 0.35. What is the probability of landing on heads?

9. Year 9 and Year 10 boys play a football match with a penalty shoot-out, so the teams cannot draw. The probability of Year 9 winning is 0.42, what is the probability of Year 10 boys winning?

10. Year 7 and Year 8 girls play a netball match with a penalty shoot-out, so the teams cannot draw. The probability of Year 8 winning is 0.76, what is the probability of Year 7 winning?

11. Ben plays a game of chess against a computer, it cannot draw. The computer is set to h

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