Examine each of the following statements and comment:
If two coins are tossed at the same time, there are 3 possible outcomes - two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is \( \frac{1}{3}. \)
Given:
If two coins are tossed at the same time, there are 3 possible outcomes - two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is \( \frac{1}{3}. \)
To do:
We have to find whether the given statement is true or false.
Solution:
When two coins are tossed simultaneously, the total possible outcomes are HH, HT, TH and TT.
This implies,
The total number of possible outcomes $n=4$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting two heads $=\frac{1}{4}$
Probability of getting two tails $=\frac{1}{4}$
Probability of getting one head and one tail $=\frac{2}{4}=\frac{1}{2}$
Therefore, the given statement is false.
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