When a die is thrown the number of possible outcomes of getting an odd number is

Solution:

We use the basic concepts of probability to find the required outcomes.

(i) Incorrect

If two coins are tossed simultaneously then,

Total possible outcomes are (H, H), (T, T), (H, T), (T, H) = 4

Number of outcomes to get two heads = (H, H) = 1

Number of outcomes to get two tails = (T, T) = 1

Number of outcomes to get any one of each = (H, T), (T, H) = 2

probability of getting two heads = Number of possible outcomes/Total number of favourable outcomes

= 1/4

probability of getting two tails = Number of possible outcomes/Total number of favourable outcomes

= 1/4

probability of getting one of each = Number of possible outcomes/Total number of favourable outcomes

= 2/4 = 1/2

It can be observed that the probability of each of the outcomes is not 1/3.

(ii) Correct

Total number of possible outcomes when a die is thrown = (1, 2, 3, 4, 5, 6)

Number of possible outcomes to get an odd number (1, 3, 5) = 3

Number of possible outcomes to get an even number (2, 4, 6) = 3

probability of getting odd number = Number of possible outcomes/Number of favourable outcomes

= 3/6 = 1/2

Thus, the probability of getting an odd number is 1/2.

Check out more about terms of probability.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 15

Video Solution:

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 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 1/2.

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 25

Summary:

The argument (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 1/3 is incorrect and the argument (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 1/2.is correct

☛ Related Questions:

Answer

Verified

Hint:Here, we will be using the concept of probability to solve the question. The probability of an event is the chance that the event occurs. Odd numbers are the natural numbers which are not divisible by 2. First, we will find the total number of outcomes when a die is rolled. We will then find the favourable outcomes of getting an odd number. We will substitute the values in the formula of probability to find the answer.Formula Used: We will use the formula for probability of an event, \[P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}\].

Complete step by step solution:

First, we will find the total number of outcomes and the number of favourable outcomes.When a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, or 6 appears on the die.Thus, we observe that the total number of outcomes is 6 when a die is rolled.Now, we need to find the probability that an odd number is obtained.Odd numbers are the natural numbers that are not divisible by 2. For example, 1, 3, 5, 7 are odd numbers.We can see that the possible odd numbers when a die is rolled are 1, 3, and 5.Therefore, we observe that the number of favourable outcomes is 3.Next, we know that the probability of an event \[E\] is given by \[P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}\].Let \[E\] be the event of getting an odd number when a die is thrown.Substituting 3 for the number of favourable outcomes and 6 for the number of total outcomes, we get\[P\left( E \right) = \dfrac{3}{6}\]Simplifying the expression, we get\[P\left( E \right) = \dfrac{1}{2}\]

\[\therefore\] The probability of getting an odd number when a die is thrown is \[\dfrac{1}{2}\] or \[0.5\].

Note:

We can also solve this problem by finding the probability of getting an even number when a die is rolled. Then, subtract it from 1 to get the probability of getting an odd number.Even numbers are the natural numbers that are divisible by 2. We can see that the possible even numbers when a die is rolled are 2, 4, and 6.Therefore, we observe that the number of favourable outcomes is 3.Next, we know that the probability of an event \[E\] is given by \[P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}\].Let \[E\] be the event of getting an even number when a die is thrown.Substituting 3 for the number of favourable outcomes and 6 for the number of total outcomes, we get\[P\left( E \right) = \dfrac{3}{6}\]Simplifying the expression, we get\[P\left( E \right) = \dfrac{1}{2}\]Therefore, we get the probability of getting an even number when a die is thrown as \[\dfrac{1}{2}\].Now, we will subtract the probability of getting an even number from 1 to get the probability of getting an odd number.Let \[O\] be the event of getting an odd number when a die is thrown.\[\begin{array}{l}P\left( O \right) = 1 - P\left( E \right)\\ = 1 - \dfrac{1}{2}\\ = \dfrac{1}{2}\end{array}\]Therefore, the probability of getting an odd number when a die is thrown is \[\dfrac{1}{2}\] or \[0.5\].

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 1/2