QUESTION 3
Easy
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?
SOLUTION
1
Record the results of 20 tosses
Suppose the results are:
| Outcome | Number of Times |
|---|---|
| Heads | 12 |
| Tails | 8 |
| Total Tosses | 20 |
2
Answer (i) and (ii)
(i) How many times did you get heads?
From the table, we see that head occurred \(12\) times.
(ii) How many times did you get tails?
From the table, we see that tails occurred \(8\) times.
From the table, we see that head occurred \(12\) times.
(ii) How many times did you get tails?
From the table, we see that tails occurred \(8\) times.
3
(iii)Calculate experimental probability of Heads
\(P(Heads) = \frac{Number\, of\, times\, heads\, occured}{Total\, number\, of\, trials} = \frac{12}{20} = \frac{3}{5}\) or \(0.6\)
4
Find probability of getting tails on one more toss
Afair coin has two equally likely outcomes: Heads or Tails
So the theoretical probability of getting tails is:
\(P(Tails) = \frac{1}{2}\) or \(0.5\).
So the theoretical probability of getting tails is:
\(P(Tails) = \frac{1}{2}\) or \(0.5\).
Concept Note
Experimental probability is based on actual observations or experiments. It is calculated by:
\(Experimental\, Probability\, = \frac{Number\, of\, times\, an\, event\, occurred}{Total\, trials}\)
A fair coin has equal chances of heads and tails. So theoretical probability of tails on any single toss is always \(\frac{1}{2}\).