Question

A box contains 26 cards with all English alphabets from A to Z.
The probability of randomly choosing the card with either 'E' or 'S' from this box is ______.

• A. 2/26
• B. 1/26
• C. 3/26
• D. 4/26

Hint:

Since a card cannot be both E and S at the same time, just add the individual probabilities of drawing E and drawing S.

Answer 1

The Correct Option is A

Step 1: Identify the total number of possible outcomes.
The box has 26 cards, one for each letter A through Z, so the total number of equally likely outcomes is 26.

Step 2: Identify the favourable outcomes.
We want the card to be either 'E' or 'S'. There is exactly 1 card labelled 'E' and exactly 1 card labelled 'S', and a single card cannot be both letters at once, so these two events cannot happen together (they are mutually exclusive). The number of favourable outcomes is \(1 + 1 = 2\).

Step 3: Apply the basic probability formula. \[P(E \text{ or } S) = \frac{\text{favourable outcomes}}{\text{total outcomes}} = \frac{2}{26}\]

Step 4: Match with the options.
This is option (A). Option (B) would only be correct if the question asked for the probability of a single specific letter. Options (C) and (D) overcount the number of favourable letters, which is not supported by the question.