JAMIA 2025 — Mathematics PYQ

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Question

JAMIA 2025 — Mathematics PYQ

JAMIA | Mathematics | 2025

The probability of getting at least one head when tossing two fair coins is :

Choose the correct answer:

Explanation

Solution

When two fair coins are tossed, the set of all possible outcomes, known as the Sample Space ( $S$ ), is:

S = \{(H, H), (H, T), (T, H), (T, T)\}

The total number of outcomes is:

n(S) = 4

We want to find the probability of the event $E$ , where we get at least one head. The outcomes favorable to this event are:

E = \{(H, H), (H, T), (T, H)\}

The number of favorable outcomes is:

n(E) = 3

Calculation

The probability $P(E)$ is defined as the ratio of favorable outcomes to the total number of outcomes:

P(E) = \frac{n(E)}{n(S)}

Substituting the values:

P(E) = \frac{3}{4}

In decimal form, this is:

P(E) = 0.75

Alternative Method (Complement Rule)

Sometimes it is easier to calculate the probability of the opposite event (getting no heads) and subtract it from $1$ :

Probability of getting no heads (i.e., getting both Tails): $P(\text{TT}) = \frac{1}{4}$
$P(\text{at least one Head}) = 1 - P(\text{no Heads})$

P(E) = 1 - \frac{1}{4} = \frac{3}{4}

Final Answer:

The probability is 3/4 or 0.75.

Choose the correct answer:

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