Example 1 · level 1
Harpreet rolls a fair six-sided die at a school fair in Nagpur. What is the probability of getting a prime number?
- 1/3
- 1/2
- 2/3
- 1
Show solution
- Favourable faces: 3 of 6.
- Probability = 3/6 = 1/2.
Answer: 1/2
ABHYAS PREP: ADVANCED QUANT · PROBABILITY
Probability with dice, coins, cards and bags
Probability = favourable outcomes ÷ total equally likely outcomes. List ordered outcomes for dice, subtract overlaps for “or”, and reduce the total after each draw when there is no replacement.
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Worked examples
Example 2 · level 2
5 fair coins are tossed together by Ananya. What is the probability of getting exactly 1 head?
- 1/32
- 5/32
- 1/6
- 31/32
Show solution
- Total outcomes: 32.
- Outcomes with exactly 1 heads: C(5, 1) = 5.
- Probability = 5/32 = 5/32.
Answer: 5/32
Example 3 · level 3
A pouch in Ayaan’s house in Guwahati has 6 blue, 2 black and 5 red pens. Two are taken out at random, one after the other, without replacement. What is the probability that at least one of them is blue?
- 5/26
- 7/26
- 120/169
- 19/26
Show solution
- P(no blue) = C(7, 2)/C(13, 2) = 21/78.
- P(at least one blue) = 1 − 21/78 = 19/26.
Answer: 19/26