Chi-keung tosses a drawing pin 32 times, and it lands point up 5 times. The experimental probability of point up is □. Answer in simplest form

5/32. Experimental probability = times point up ÷ tosses = 5 ÷ 32 = 5/32.

Which of these can't be the probability of an event? A. 5/8 B. 1 C. 11/8 D. 0 Choose the right answer

C. 11/8. A probability lies from 0 to 1 (both included), and 11/8 is more than 1.

A fair die is rolled 90 times. A 3 should come up about □ times.

15. P(3) = 1/6, so the expected count = 90 × 1/6 = 15.

Probability · Ages 14–15

What a probability means

0 ≤ P ≤ 1; P(not) = 1 − P; experimental = times ÷ trials.

How to do it

Method

0 ≤ P ≤ 1; P(not) = 1 − P; experimental = times ÷ trials

P(rain) = 310, P(no rain) = 1 − 310 = 710

Another way

From the counts

120 rolls × 16 = 20 times

In full

A probability measures how likely something is, as a number from 0 to 1: an impossible event's probability is 0, a certain event's 1, and any other's between, so 54 or −0.2 can never be one. An event happening and not happening have probabilities adding to 1: P(not A) = 1 − P(A). If the chance of rain is 310, the chance of no rain is 1 − 310 = 710. An experiment gives an experimental probability: the times the event happened ÷ the number of trials. A drawing pin tossed 50 times lands point up 18 times: 1850 = 925. The other way round, a probability estimates a count: expected count = trials × probability. A fair die rolled 120 times should show a 6 about 120 × 16 = 20 times. An experimental probability needn't equal the theoretical one, but it usually gets closer the more trials there are.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
Chi-keung tosses a drawing pin 32 times, and it lands point up 5 times. The experimental probability of point up is .
Answer in simplest form
Show the answer and working
Answer: 532
Experimental probability = times point up ÷ tosses = 5 ÷ 32 = 532.
Example 2
Which of these can't be the probability of an event?
- A. 58
- B. 1
- C. 118
- D. 0
Choose the right answer
Show the answer and working
Answer: C. 118
A probability lies from 0 to 1 (both included), and 118 is more than 1.
Example 3
A fair die is rolled 90 times. A 3 should come up about times.
Show the answer and working
Answer: 15
P(3) = 16, so the expected count = 90 × 16 = 15.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Chi-keung tosses a drawing pin 28 times, and it lands point up 17 times. The experimental probability of point up is .
Answer in simplest form
Answer:
2.Which of these can't be the probability of an event?
- A. 0
- B. 34
- C. 95
- D. 1
Choose the right answer
Answer:
3.P(A) = 14, so P(not A) = 34.
True or false?
Answer:
4.May tosses a fair coin 20 times and gets 19 heads. Which statement is right?
- A. The theoretical probability of heads is 1920
- B. The experimental probability of heads is 1920; the theoretical one is still 12
- C. The coin can't be fair
- D. Further tosses will make up for it, so heads end at exactly half
Choose the right answer
Answer:
5.Tomorrow will be exactly one of sunny, cloudy or rainy. The probability of sunny is 18 and of cloudy 13. The probability of rainy is .
Answer in simplest form
Answer:

All the answers

1. 1728
2. C. 95
3. True
4. B. The experimental probability of heads is 1920; the theoretical one is still 12
5. 1324

Free worksheet: What a probability meansWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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