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# Ex.15.1 Q25 Probability Solution - NCERT Maths Class 10

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## Question

Which of the following arguments are correct and which are not correct?

(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 of an odd number or an even number. Therefore, the probability of getting an odd number is $$1/2$$

Video Solution
Probability
Ex 15.1 | Question 25

## Text Solution

Reasoning:

Probability of an event

$=\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} }$

Steps:

(i) Incorrect

If two coins are tossed simultaneously then ,

Total possible outcomes are

$$\text{(H,H), (T,T), (H,T), (T,H)} = 4$$

No of outcomes to get two heads $$=\text{(H,H)}=1$$

No of outcomes to get two tails $$=\text{(T,T)}= 1$$

No of outcomes to one of each$$=\text{(H,T), (T,H) }= 2$$

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\& =\frac{1}{4} \end{align}

Probability of getting two tails

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\& =\frac{1}{4} \end{align}

Probability of getting one of each

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ & =\frac{2}{4}\\&=\frac{1}{2} \end{align}

It can be observed that,

Thus, the probability of each of the outcome is not \begin{align}\frac{1}{3}.\end{align}

(ii) correct

Total no of possible outcomes when a dice is thrown $$= \left( \text{1,2,3,4,5,6} \right)$$

No of possible outcomes to get odd number $$\left( \text{1,3,5} \right)=3$$

No of possible outcomes to get even number $$\left( \text{2,4,6} \right)=3$$

probability of getting odd number

\begin{align}& =\frac{\begin{bmatrix} \text { Number of}\\ \text{ possible outcomes }\end{bmatrix} }{ \begin{bmatrix}\text { Total no of} \\ \text{favorable outcomes} \end{bmatrix} } \\ & =\frac{3}{6}\\&=\frac{1}{2} \end{align}

Thus, the probability of getting an odd number is \begin{align}\frac{1}{2}.\end{align}

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