Data and probability · Ages 14–15

What a probability means worksheet

Part of: Probability

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Data and probability · Ages 14–15

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.P(A) = 712, so P(not A) = .
Answer in simplest form
Answer:
2.Tsz-hin tosses a drawing pin 28 times, and it lands point up 5 times. The experimental probability of point up is .
Answer in simplest form
Answer:
3.P(A) = 57, so P(not A) = .
Answer in simplest form
Answer:
4.A mobile game player records 55 card draws, 15 of them rare cards. The experimental probability of a rare card is , and of not getting one .
Fill in each blank
Answer:
5.A fair die is rolled 108 times. A 1 should come up about times.
Answer:
6.A fair die is rolled 216 times. A 4 should come up about times.
Answer:
7.A mobile game player records 112 card draws, 28 of them rare cards. The experimental probability of a rare card is , and of not getting one .
Fill in each blank
Answer:
8.Tomorrow will be exactly one of sunny, cloudy or rainy. The probability of sunny is 12 and of cloudy 15. The probability of rainy is .
Answer in simplest form
Answer:
9.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:

13.Ming rolls a fair die 60 times and gets a 1 on 12 of them. In this experiment, the experimental probability of a 1 is greater than the theoretical one.
True or false?
Working:
Answer:
14.A café records 120 customers, 40 of whom order milk tea. From this, the probability the next one orders it is about ; with 480 customers expected tomorrow, about will order milk tea.
Fill in each blank
Working:
Answer:
15.Ka-lok rolls a fair die 150 times and gets a 6 on 21 of them. The experimental probability of a 6 is , and the theoretical one .
Fill in each blank
Working:
Answer:
16.A factory checks 100 toys and finds 14 faulty. Today it made 800. About how many are faulty?
Working:
Answer:
17.The weather forecast gives a 10% chance of rain tomorrow. What is the probability of no rain, as a fraction in its simplest form?
Answer in simplest form
Working:
Answer:
18.A factory checks 200 toys and finds 11 faulty. Today it made 400. About how many are faulty?
Working:
Answer:

Show the answers and working

What a probability means worksheet: Answers and working

1. 512
P(A) + P(not A) = 1, so P(not A) = 1 − 712 = 512.
2. 528
Experimental probability = times point up ÷ tosses = 5 ÷ 28 = 528.
3. 27
P(A) + P(not A) = 1, so P(not A) = 1 − 57 = 27.
4. 311, 811
15 ÷ 55 = 311; not rare 55 − 15 = 40 times, 40 ÷ 55 = 811. The two add to 1.
5. 18
P(1) = 16, so the expected count = 108 × 16 = 18.
6. 36
P(4) = 16, so the expected count = 216 × 16 = 36.
7. 14, 34
28 ÷ 112 = 14; not rare 112 − 28 = 84 times, 84 ÷ 112 = 34. The two add to 1.
8. 310
Exactly one of the three happens, so their probabilities add to 1: P(rainy) = 1 − 12 − 15 = 310.
9. 1324
Exactly one of the three happens, so their probabilities add to 1: P(rainy) = 1 − 18 − 13 = 1324.

10. A. 107
A probability lies from 0 to 1 (both included), and 107 is more than 1.
11. True
P(not A) = 1 − 18 = 78.
12. C. The experimental probability of heads is 1940; the theoretical one is still 12
The experimental probability, 19 ÷ 40, comes from the tosses; the theoretical one, 12, from the coin being fair. With more tosses they usually get closer.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. True
The theoretical 16 means about 10 of 60; there were 12. Only more than 10 makes the experimental one larger.
14. 13, 160
Experimental probability = 40 ÷ 120 = 13; expected number = 480 × 13 = 160.
15. 750, 16
Experimental = 21 ÷ 150 = 750; a fair die's 6 outcomes are equally likely, so the theoretical one is 16. They needn't match.
16. 112 toys
The experimental probability of a fault is 14100; 800 × 14100 = 112.
17. 910
P(no rain) = 1 − 10% = 90% = 90100 = 910.
18. 22 toys
The experimental probability of a fault is 11200; 400 × 11200 = 22.

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