# Probability - Class 10 - Mathematics

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## Extra Questions - Probability | NCERT | Mathematics | Class 10

Two dice are thrown at the same time. Find the probability of getting different numbers on the dice.

(A) $\frac{2}{3}$

(B) $\frac{5}{6}$ (C) $\frac{1}{6}$

(D) $\frac{1}{3}$

The correct choice is **(B) $\frac{5}{6}$**.

First, let's consider the **total number of outcomes** when two dice are thrown. Each die has 6 faces, leading to:
$$
36\ \text{(since } 6 \times 6 = 36\text{)}
$$

Next, consider the outcomes where both dice show the **same number**:
$$
{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
$$
This gives us **6 outcomes** where the numbers are the same.

The probability of an event $E$ is given by: $$ P(E) = \frac{\text{Number of outcomes favorable to } E}{\text{Number of all possible outcomes of the experiment}} $$

Applying this to the probability of getting the **same number** on both dice:
$$
P(\text{Same number}) = \frac{6}{36} = \frac{1}{6}
$$

To find the probability of getting **different numbers** on both dice, we subtract the probability of getting the same number from 1 (total probability):
$$
P(\text{Different numbers}) = 1 - P(\text{Same number}) = 1 - \frac{1}{6} = \frac{5}{6}
$$

Therefore, the probability of getting different numbers on both dice is $\frac{5}{6}$.

Can the experimental probability of an event be greater than 1? Justify your answer.

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In a school, there were five teachers: $A$ and $B$ were teaching Hindi and English; $C$ and $B$ were teaching English and Geography; D and A were teaching Mathematics and Hindi; E and B were teaching History and French.

D, B, and A were teaching which of the following subjects?

A. English only B. Hindi and English C. Hindi only D. English and Geography