# Probability - Class 11 - Mathematics

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## Extra Questions - Probability | NCERT | Mathematics | Class 11

Two coins are tossed simultaneously 200 times and the number of heads is recorded as follows:

\begin{tabular}{|c|c|} \hline Number of heads & Frequency \ \hline 0 & 65 \ \hline 1 & 85 \ \hline 2 & 50 \ \hline \end{tabular}

What is the probability of 1 head appearing?

A) 0.4 B) 0.5 C) 0.425 D) 0.75

```
**Answer: C) 0.425**
To determine the **probability of 1 head appearing**, we use the formula for probability $P(E)$ where $E$ is the event of interest:
$$
P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}
$$
In this scenario, the event $E$ (1 head appearing) occurred 85 times out of 200 total coin tosses. Applying the formula, we get:
$$
P(E) = \frac{85}{200} = 0.425
$$
Thus, the **probability that exactly one head appears** when tossing two coins simultaneously and observing the outcomes across 200 tosses is **0.425**.
```

"A four-digit number (ranging from 0000 to 9999) is said to be lucky if the sum of its first two digits is equal to the sum of its last two digits. If a four-digit number is picked at random, then the probability that it is a lucky number is:

A. 0.07

B. 0.067

C. 0.67

D. 0.6"

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The last page number on the textbooks of different subjects in a class is given. \begin{tabular}{|c|c|} \hline Subject & Page Number \ \hline English & 203 \ \hline Hindi & 203 \ \hline Maths & 152 \ \hline Physics & 177 \ \hline Chemistry & 225 \ \hline Biology & 172 \ \hline Computer Sci. & 185 \ \hline History & 203 \ \hline Geography & 172 \ \hline Moral Sci. & 267 \ \hline \end{tabular}

Find the probability that the last page number ends in (i) an odd number (ii) an even number (iii) a multiple of 3. [4 MARKS]

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8 coins are tossed simultaneously. The probability of getting at least 6 heads is [AISSE 1985; MNR 1985; MP PET 1994]

A) $\frac{57}{64}$ B) $\frac{229}{256}$ C) $\frac{7}{64}$ D) $\frac{37}{256}$