Toss a coin 20 times and record the result each time (heads or tails).
- (i) How many times did you get heads?
- (ii) How many times did you get tails?
- (iii) Calculate the experimental probability of getting heads.
- (iv) If you toss the coin once more, what is the probability of getting tails?
Step-by-step solution
Idea: Experimental probability = Number of times the event occurredTotal number of trials. The next toss is a fresh, independent trial, so its probability is the theoretical 12.
(i) How many times did you get heads?
- Record the results in a table. A sample run of 20 tosses:
H T T H H T H H T H
T H H T T H T H H T
(Your own list will be different; use your own counts in each part.) - Count the Hs in your record. In the sample run there are 11 heads.½ mark
(ii) How many times did you get tails?
- Tails = 20 − 11 = 9. (Count them to check: there are 9 Ts.)½ mark
(iii) Calculate the experimental probability of getting heads.
- Experimental P(heads) = Number of headsTotal number of tosses = 1120½ mark
- = 0.55 (55%). With your own counts, use your number of heads20.½ mark
(iv) If you toss the coin once more, what is the probability of getting tails?
- The next toss is independent of the first 20: the coin has no memory. Heads and tails are still equally likely.½ mark
- P(tails) = 12 = 0.5. (The experimental 0.45 for tails in the sample run describes the past 20 tosses; it does not change the chance on the next toss.)½ mark
Check: Your heads and tails must add up to 20, and your experimental P(heads) + P(tails) must add up to 1 (0.55 + 0.45 = 1 ✓). Most people get between 7 and 13 heads in 20 tosses.
Answer to write in the exam
(i)
Sample record: H T T H H T H H T H T H H T T H T H H T
∴ Number of heads = 11
(ii)
Tails = 20 − 11
∴ Number of tails = 9
(iii)
Experimental P(heads) = Number of headsTotal tosses = 1120
∴ Experimental P(heads) = 0.55
(iv)
Each toss is independent; H and T equally likely.
∴ P(tails) = 12
Common mistakes that cost marks
- Using the experimental value (e.g. 0.45) as the answer to (iv). For the next toss of a fair coin the probability is 12.
- Dividing by the number of tails instead of by the total 20 in (iii).
- Expecting exactly 10 heads and thinking the coin is unfair if you get 12. With only 20 tosses, results like 12 and 8 are normal.
How this can come in the exam
A coin is tossed 30 times and shows heads 18 times. The experimental probability of getting tails is
- 0.4
- 0.5
- 0.6
- 1830
Show answer
(A) 0.4
Tails = 30 − 18 = 12; 1230 = 0.4.
Assertion (A): A coin tossed 40 times showed heads 26 times, so the experimental probability of heads is 0.65.
Reason (R): For a fair coin, the experimental probability of heads is always exactly 0.5.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(C) A is true but R is false.
A is true: 2640 = 0.65. R is false: experimental results vary; only the theoretical probability is exactly 0.5.
Try one yourself
Rahul tossed a coin 25 times and got 14 heads. Find the experimental probability of (a) heads, (b) tails. What is the probability of heads on his 26th toss?
Show answer
(a) 1425 = 0.56. (b) 1125 = 0.44. 26th toss: 12.
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