Question

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 \[\dfrac{1}{3}\].

(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 \[\dfrac{1}{2}\].

Answer 1

Hint: Write the set of all possible outcomes in each of the given cases. Calculate the probability of each of the events using the fact that probability of any event is the ratio of number of favourable outcomes to the total number of possible outcomes. Check whether each of the given statements is correct or not.

Complete step by step answer:
We have to check if each of the given statements regarding probability of certain events is correct or not.

We know that probability of any event is the ratio of the number of favourable outcomes to the total number of possible outcomes. We will calculate the probability of the events in each case and check if it is correct or not.

(i) We have tossed two coins simultaneously. So, the possible set of outcomes is \[\left\{ HH,TT,HT,TH \right\}\].

We can get two heads or two tails only once, while one head and one tail twice.

So, the probability of getting two heads \[=\dfrac{1}{4}\].

Similarly, the probability of getting two tails \[=\dfrac{1}{4}\].

Probability of getting one head and one tail \[=\dfrac{2}{4}=\dfrac{1}{2}\].

Thus, the statement given in the question that probability of getting two heads or two tails or one head and one tail is \[\dfrac{1}{3}\] is incorrect as each of the events have a different probability which is not equal to \[\dfrac{1}{3}\].

(ii) We will now calculate the probability of getting an odd number and an even number when a dice is rolled.

The possible set of events are \[\left\{ 1,2,3,4,5,6 \right\}\]. Set of events for getting an odd number is \[\left\{ 1,3,5 \right\}\] and the set of events for getting an even number is \[\left\{ 2,4,6 \right\}\].

The probability of getting an odd number \[=\dfrac{3}{6}=\dfrac{1}{2}\].

Hence, the statement given in the question is correct.

Note: Probability of any event describes how likely an event is to occur or how likely it is that a proposition is true. The value of probability of any event always lies in the range \[\left[ 0,1 \right]\] where having 0 probability indicates that the event is impossible to happen, while having probability equal to 1 indicates that the event will surely happen. We must remember that the sum of probability of occurrence of some event and probability of non-occurrence of the same event is always 1.