Suppose you roll a die 50 times, and it lands on a 4 exactly 8 times.
Step-by-step solution
To find: The experimental probability (relative frequency) of rolling a 4
Idea: Experimental probability uses what actually happened: Experimental Probability = Number of times the event occurredTotal number of trials.
- Event: rolling a 4. It occurred 8 times. Total number of trials = 50.½ mark
- Experimental probability of rolling a 4 = Number of times a 4 came upTotal number of rolls = 850½ mark
- 850 = 16100 = 0.16, which is 16%.½ mark
- This fraction is also called the relative frequency of rolling a 4: the relative frequency of rolling a 4 is 850 = 0.16. It is based on actual data, not on a theoretical prediction.½ mark
Check: 0.16 × 50 = 8 ✓, which is the number of 4s observed.
Answer to write in the exam
Number of times 4 occurred = 8; total trials = 50
Experimental probability = Number of times the event occurredTotal number of trials
= 850 = 0.16
∴ Experimental probability (relative frequency) of rolling a 4 = 0.16 or 16%
Common mistakes that cost marks
- Writing 842 (dividing by the number of times a 4 did not come up). Always divide by the total number of trials, 50.
- Giving 16 as the answer. 16 is the theoretical probability; the question is about what actually happened in 50 rolls.
- Converting 0.16 to 1.6% or 0.16%. To change a decimal to a percentage, multiply by 100: 0.16 × 100 = 16%.
How this can come in the exam
A die is thrown 80 times and a 2 comes up 12 times. The relative frequency of getting a 2 is
- 0.12
- 0.15
- 0.2
- 16
Show answer
(B) 0.15
1280 = 320 = 0.15.
A coin is tossed 150 times and lands heads 84 times. Find the experimental probability of (a) heads, (b) tails.
Show answer
(a) P(heads) = 84150 = 0.56. (b) Tails came up 150 − 84 = 66 times, so P(tails) = 66150 = 0.44. Check: 0.56 + 0.44 = 1.Try one yourself
A die is rolled 60 times and a 5 comes up 9 times. Find the experimental probability of rolling a 5, as a decimal and a percentage.
Show answer
960 = 0.15 = 15%.
More questions like this
- If you roll a standard 6-sided die, what is the theoretical probability of getting a 4?
- A letter is picked at random from the word ‘PROBABILITY’. What is the probability of picking the letter B?
- Suppose you anonymously collect information regarding the favourite fruit of 50 students in your class. Let us assume that the results are: 20 students like mango, 15 students like apples, 10 students like bananas, and 5 students like grapes. Let us play a game! Suppose we randomly pick one student from the class and try to guess their favourite fruit. What’s the probability that the student’s favourite fruit is mango?
- If I have rolled a 4 on a die 8 times in succession, the probability of rolling a 4 again is still only ≈ 0.16 (assuming the die is fair). Probability does not tell you what will happen next but predicts what will happen in the long run.
- Let us say you are playing Snakes and Ladders, and you are rolling a fair 6-sided die to move. You have just rolled the die three times in a row, and each time you got a 6. Now, you think: ‘I have already rolled three 6s — there is no way I will get a 6 again on the next roll!’