The mean of the number of heads in the two tosses of a coin is Option 1: 1 Option 2: 2 Option 3: 4 Option 4: 5

Answer: 1. Solution: When tossing a coin 2 times, there are 4 possible outcomes:, Outcome, First Toss, Second Toss, Number of Heads, 1, H, H, 2, 2, H, T, 1, 3, T, H, 1, 4, T, T, 0, Each outcome is equally likely. The probability distribution for the number of heads: 0 heads: Occurs 1 time (TT) → Probability = 1/4 1 head: Occurs 2 times (HT, TH) → Probability = 2/4 2 heads: Occurs 1 time (HH) → Probability = 1/4 Mean = (Each value) x (Its probability) Mean = (0 x 1/4) + (1 x 2/4) + (2 x 1/4) Mean = 0 + 2/4 + 2/4 Mean = 4/4 Mean = 1 Therefore, the mean number of heads in two tosses of a coin is 1.

Algebra

Probability

Easy

applied

The mean of the number of heads in the two tosses of a coin is

✅ Correct Option: 1

When tossing a coin 2 times, there are 4 possible outcomes:

Outcome	First Toss	Second Toss	Number of Heads
1	H	H	2
2	H	T	1
3	T	H	1
4	T	T	0

Each outcome is equally likely.

The probability distribution for the number of heads:

0 heads: Occurs 1 time (TT) → Probability = $\frac{1}{4}$

1 head: Occurs 2 times (HT, TH) → Probability = $\frac{2}{4}$

2 heads: Occurs 1 time (HH) → Probability = $\frac{1}{4}$

Mean = (Each value) $\times$ (Its probability)

Mean = $(0 \times \frac{1}{4}) + (1 \times \frac{2}{4}) + (2 \times \frac{1}{4})$

Mean = $0 + \frac{2}{4} + \frac{2}{4}$

Mean = $\frac{4}{4}$

Mean = $1$

Therefore, the mean number of heads in two tosses of a coin is $1$ .

2025: 22 May Shift 2

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$ , and $E(X^2)=E(X)$ , then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

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x	0	1	2	3	4
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The value of K is:

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A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$ . They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed is of type $A_2$ given that seed germinate.

The mean of the number of heads in the two tosses of a coin is

Solution

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