KJSEA 2025 Maths Q20 — Probability of Picking the Letter E
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The Question
“The letters of a word were each written on a separate card, giving 11 cards in total. Among these 11 letters, the letter E appears three times. Asha picks one card at random. What is the probability that she picks a card showing the letter E? The multiple-choice answer is C, three elevenths.”
Count the total number of cards
Every letter of the word is written on its own card, so the number of cards equals the number of letters. Counting all the letters gives eleven, and because each card is equally likely to be chosen, this is the total number of possible outcomes.
Count the favourable cards
A favourable outcome is any card that shows the letter E. Reading through the letters, the letter E occurs three times, so three of the eleven cards are the ones we want.
Apply the probability formula
The probability of an event is the number of favourable outcomes divided by the total number of equally likely outcomes. Here that is the number of E cards over the total number of cards, which gives three out of eleven. This fraction does not simplify because 3 and 11 share no common factor.
Final Result
The probability that Asha picks a card showing the letter E is three elevenths, which is option C.
Why this method works
Each card is drawn at random from the same pile, so all eleven cards have an equal chance of being selected. When outcomes are equally likely, probability is simply the share of outcomes that count as a success. Since three of the eleven equally likely cards carry the letter E, the chance of drawing an E is exactly that share, three out of eleven. The fraction stays as 3/11 because 3 is prime and does not divide 11, so there is no smaller equivalent form.
The three letter counts must fit the whole: 3 E cards plus 8 non-E cards equals 11, and the probabilities 3/11 and 8/11 add to 1, confirming the answer is consistent.