# Probability - Class 12 - Mathematics

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## Extra Questions - Probability | NCERT | Mathematics | Class 12

A dice is rolled once. The following event is described. $$ A={\text{Getting } 5 \text{ or } 6} $$

Which of the following is the complement of $A$?

A ${1, 2, 5}$

B ${1, 2, 6}$

C ${1, 2, 3}$

D ${1, 2, 3, 4}$

The correct answer is **D** ${1, 2, 3, 4}$.

When a dice is rolled, the possible outcomes form a **sample space S**, which is:
$$
S = {1, 2, 3, 4, 5, 6}
$$

The given event $A$ represents rolling a 5 or a 6. Therefore: $$ A = {5, 6} $$

The **complement of $A$**, denoted as $A^c$, includes all outcomes in the sample space $S$ that are not in $A$. This is calculated by:
$$
A^c = S - A = {1, 2, 3, 4, 5, 6} - {5, 6}
$$
Resulting in:
$$
A^c = {1, 2, 3, 4}
$$

This means that **option D**, ${1, 2, 3, 4}$, is the correct complement of the event $A$ where only the outcomes 5 and 6 are excluded.

The probability that the $13^{\text{th}}$ day of a randomly chosen month is a Friday is

(A) $\frac{1}{12}$

B $\frac{2}{3}$

C) $\frac{1}{84}$

D) None

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A divisor of 1200 is selected at random. Find the probability that it is even.

A) $\frac{4}{5}$

B) $\frac{3}{5}$

C) $\frac{3}{4}$

D) $\frac{12}{13}$

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A weather station recorded the temperatures of a place over a period of 7 days as follows: \begin{tabular}{ll} Day & Temperature ($^{\circ}$C) \ Monday & 45 \ Tuesday & 38 \ Wednesday & 40 \ Thursday & 42 \ Friday & 41 \ Saturday & 37 \ Sunday & 36 \end{tabular}

Find the probability of a day having a temperature of more than $40^{\circ}$C.

(A) $\frac{2}{7}$

(B) $\frac{5}{7}$

(C) $\frac{4}{7}$

(D) $\frac{3}{7}