Data and probability · Ages 14–15
Probability worksheet
Covers: Certain, impossible and random events, What a probability means, Equally likely outcomes, Relative frequency and expected frequency, Listing outcomes in a table, Tree diagrams, Probability word problems, Expected value, Fair games and expected gain
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Probability worksheet
Data and probability · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.P(A) = 211, so P(not A) = .
Answer in simplest form
Answer:
2.Ka-yee tosses a drawing pin 20 times, and it lands point up 5 times. The experimental probability of point up is .
Answer in simplest form
Answer:
3.A whole number from 1 to 12 is chosen at random. The probability of a multiple of 6 is .
Answer in simplest form
Answer:
4.A spinner has 8 equal parts with the numbers shown. Spun once, the probability it stops on an odd number is .
Answer in simplest form
Answer:
5.A bag holds red, yellow and blue balls. Ka-lok draws one at random, notes its colour and puts it back, 250 times in all: red 188 times, yellow 57 times, and blue the rest. Blue's frequency is , and its relative frequency .
Fill in each blank
Answer:
6.There are 4 roads from A to B and 5 from B to C. Going from A to C through B, there are different routes; choosing one at random, the probability of Ming's favourite is .
Fill in each blank
Answer:
7.A fair die is rolled: a 6 wins 58 dollars, a 1 wins 14 dollars, anything else nothing. The probability of a 6 is , and the expected prize dollars.
Fill in each blank
Answer:
8.One play costs 3 dollars. A die is rolled: a 6 wins 18 dollars, anything else nothing. What is the expected gain from one play, in dollars (a loss as a negative number)?
Answer:
Part B: Choose, or true or false (2 marks each)
9.An ordinary die is rolled once. Which of these is a certain event?
- A. Rolling a number less than 4
- B. Rolling a number less than 7
- C. Rolling a 7
- D. Rolling an odd number
Choose the right answer
Answer:
10.An ordinary die is rolled once. Which of these is an impossible event?
- A. Rolling an even number
- B. Rolling a number less than 7
- C. Rolling a 9
- D. Rolling a 3
Choose the right answer
Answer:
11.Rolling two dice, a sum of 4 is exactly as likely as a sum of 11.
True or false?
Answer:
12.A whole number from 1 to 38 is chosen at random. What is the probability of a multiple of 2 or 7?
- A. 1119
- B. 1019
- C. 119
- D. 1219
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.A drawer holds socks in 4 colours, 4 of each, all mixed up. In the dark, at least how many must be taken to be sure of two the same colour?
Working:
Answer:
14.Ka-yan rolls a fair die 120 times and gets a 1 on 24 of them. In this experiment, the experimental probability of a 1 is greater than the theoretical one.
True or false?
Working:
Answer:
15.Ming rolls a die 600 times: a 1 110 times, a 2 109 times, a 3 109 times, a 4 93 times, a 5 92 times, and a 6 the rest. A 6 came up times, a relative frequency of (as a fraction in its simplest form).
Fill in each blank
Working:
Answer:
16.Ka-lok plays a game with a friend: two dice are rolled, and if their product is a multiple of 3, Ka-lok wins. What is the probability Ka-lok wins?
Answer in simplest form
Working:
Answer:
17.A pencil case holds 3 red ballpoint pens and 7 blue. May takes two at random, one after the other, without putting any back. What is the probability both are blue?
Answer in simplest form
Working:
Answer:
18.A stall game rolls a die: a 1 wins 23 dollars, a 6 wins 43 dollars, anything else nothing. For the game to be fair, what should one play cost?
- A. 11 dollars
- B. 33 dollars
- C. 43 dollars
- D. 12 dollars
Choose the right answer
Working:
Answer:
Show the answers and working
Probability worksheet: Answers and working
Part A: Working out and filling in
1. 911
P(A) + P(not A) = 1, so P(not A) = 1 − 211 = 911.
2. 14
Experimental probability = times point up ÷ tosses = 5 ÷ 20 = 14.
3. 16
12 ÷ 6 has whole part 2, so there are 2 multiples of 6: 212 = 16.
4. 12
4 of the 8 equal parts are odd: 48 = 12.
5. 5, 0.02
Blue: 250 − 188 − 57 = 5 times; relative frequency = 5 ÷ 250 = 0.02.
6. 20, 120
The tree splits into 4, each into 5: 4 × 5 = 20 routes, one of them the favourite: 120.
7. 16, 12
E = 58 × 16 + 14 × 16 + 0 × 46 = (58 + 14) ÷ 6 = 12.
8. 0 dollars
Expected prize = 18 × 16 = 3; expected gain = 3 − 3 = 0.
Part B: Choose, or true or false
9. B. Rolling a number less than 7
Every one of 1 to 6 is less than 7, so whatever comes up, the event happens.
10. C. Rolling a 9
A die shows only 1 to 6, never 9, so rolling a 9 can't happen.
11. False
A sum of 4 fills 3 cells and 11 fills 2. Two sums match only when they add to 14.
12. A. 1119
19 + 5 − 2 of them, over 38.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 5 socks
At worst the first 4 are all different colours; the next, number 5, must match one.
14. True
The theoretical 16 means about 20 of 120; there were 24. Only more than 20 makes the experimental one larger.
15. 87, 29200
Sixes: 600 − (110 + 109 + 109 + 93 + 92) = 87; relative frequency = 87 ÷ 600 = 29200.
16. 59
In a table of products, 20 of the 36 cells are multiples of 3: 2036 = 59.
17. 715
First blue 710, second blue 69: 710 × 69 = 715.
18. A. 11 dollars
Fair means price = expected prize = (23 + 43) × 16 = 11 dollars.
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