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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.

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