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Worksheet: Simulations of Probability

Q1:

Two coins are tossed 76 times. The upper faces are observed, and the results are recorded in this table. Determine the experimental probability of getting two tails as a fraction in its simplest form.

Tails 0 1 2
Number of Occurrences 32 28 16
  • A 8 1 9
  • B 7 1 9
  • C1
  • D 4 1 9
  • E 1 2

Q2:

A coin is biased with a 5 5 % chance of getting tails for every random toss. Estimate the probability of getting exactly 55 heads in 100 tosses of a coin.

Q3:

A number cube is rolled 127 times. The results are recorded in the following table. What is the experimental probability of rolling a number greater than 4?

Number 1 2 3 4 5 6
Occurrence 21 21 14 29 15 27
  • A 2 9 1 2 7
  • B 7 1 1 2 7
  • C 2 1 1 2 7
  • D 4 2 1 2 7
  • E 5 6 1 2 7

Q4:

A survey of 92 people found that 55 people support Team A, 30 people support Team B, and 7 people support neither. What is the probability that a person supports Team A?

  • A 1 5 4 6
  • B 7 9 2
  • C 5 5 8 2
  • D 5 5 9 2
  • E 5 5 1 0 2

Q5:

A sample of 64 people found that 36 of them watch Channel A, 29 of them watch Channel B, and 11 watch both channels. What is the probability that a random person from the sample only watches Channel A?

  • A 9 3 2
  • B 9 1 6
  • C 2 9 6 4
  • D 2 5 6 4
  • E 2 5 5 4

Q6:

A factory produces two types of televisions and wants to decide how many of each to produce. The table shows the sales of a sample of 50 TV sets from each of 5 shopping malls. If the factory is going to produce 6 000 TV sets in total, how many should be of Type B?

Number of Shopping Mall 1 2 3 4 5
Sales of Type A 16 36 34 14 15
Sales of Type B 34 14 16 36 35
  • A 4 320
  • B 2 760
  • C 1 680
  • D 3 240

Q7:

A company that manufactures light bulbs tests a sample of 1000 light bulbs to determine their lifespan. The results are shown in the table. What is the probability that a light bulb lasts at least 400 hours?

𝐻 (Maximum Working Hours) Less than 150 1 5 0 𝐻 < 4 0 0 4 0 0 𝐻 < 1 0 0 0 More than 1000
Number of Lamps 100 320 270 310
  • A 2 1 5 0
  • B 2 7 1 0 0
  • C 3 1 1 0 0
  • D 2 9 5 0
  • E 9 1 0

Q8:

Three fair coins are flipped. What is the probability that as many heads as tails appear?

Q9:

A life insurance company used a sample of 4 000 men between the ages of 50 and 60 to find the probability of a man dying between these ages. Given that 17 men in the sample died, calculate the experimental probability of a man dying between the ages of 50 and 60.