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Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes- two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.
(ii) If a die is thrown, there are two possible outcomes- an odd number or an even number. Therefore, the probability of getting an odd number is $\frac{1}{2}$.
Given:
If two coins are tossed simultaneously there are three possible outcomes- two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is $\frac{1}{3}$.
To do:
We have to find whether the given statements are true or false.
Solution:
(i) 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.
(ii) When a die is thrown, the total possible outcomes are 1, 2, 3, 4, 5 and 6.
This implies,
The total number of possible outcomes $n=6$.
We know that,
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting an odd number $=\frac{3}{6}=\frac{1}{2}$
Therefore, the given statement is true.