Example 1 · level 1
A card is drawn at random from a well-shuffled pack of 52. Find the probability that it is a red card. (Answer as a fraction.)
Show solution
- Favourable = 26, total = 52.
- P = 26/52 = 1/2.
Answer: 1/2
CA FOUNDATION: QUANTITATIVE APTITUDE · PROBABILITY
Classical probability: dice, cards and balls
P(E) = favourable outcomes ÷ total equally likely outcomes. Two dice have 36 outcomes; a pack has 52 cards.
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Worked examples
Example 2 · level 2
Two fair dice are thrown. What is the probability that the sum is 6? (Answer as a fraction.)
Show solution
- Pairs: (1,5), (2,4), (3,3), (4,2), (5,1) → 5 outcomes.
- P = 5/36.
Answer: 5/36
Example 3 · level 3
A bag has 3 red and 4 blue balls. Two balls are drawn together at random. Find the probability that both are red. (Answer as a fraction.)
Show solution
- Favourable = 3C2 = 3.
- Total = 7C2 = 21.
- P = 3/21 = 1/7.
Answer: 1/7