# Examine each of the following statements and comment:

Question:

Examine each of the following statements and comment:

(i) 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 1/3.

(ii) If a die in thrown once, there are two possible outcomes − an odd number or an even number. Therefore, the probability of obtaining an odd number is 1/2 and the probability of obtaining an even number is 1/2.

Solution:

(i)

Incorrect

When two coins are tossed, the possible outcomes are (H, H), (H, T), (T, H), and (T, T). It can be observed that there can be one of each in two possible ways − (H, T), (T, H).

Therefore, the probability of getting two heads is $\frac{1}{4}$, the probability of getting two tails is $\frac{1}{4}$, and the probability of getting one of each is $\frac{1}{2}$.

It can be observed that for each outcome, the probability is not $\frac{1}{3}$.

(ii)

Correct

When a dice is thrown, the possible outcomes are 1, 2, 3, 4, 5, and 6. Out of these, 1, 3, 5 are odd and 2, 4, 6 are even numbers.

Therefore, the probability of getting an odd number is $\frac{1}{2}$.

Similarly, the probability of getting an even number is $\frac{1}{2}$.