Practice Questions
Concept Explanation
Probability measures how likely an event is, on a scale from 0 to 1. For equally likely outcomes, probability is the ratio of favourable outcomes to total outcomes.
Key Formula
- P(E) = Number of favourable outcomes / Total number of outcomes
- 0 ≤ P(E) ≤ 1
- P(certain event) = 1; P(impossible event) = 0
Example
A fair die has 6 equally likely faces. P(getting 4) = 1/6.
Common Trap
Count only equally likely outcomes. If outcomes are not equally likely, simple counting does not give correct probability.
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Q1 EasyA bag has 3 red and 7 blue balls. One ball is drawn at random. What is the probability that the ball drawn is red?ExplanationP(E) = favourable / total. Favourable red balls = 3, total balls = 10. P(red) = 3/10. Hence the answer is 3/10.
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Q2 EasyA fair six-sided die is rolled. What is the probability of getting an even number?ExplanationP(E) = favourable / total. Even faces: 2, 4, 6 → 3 favourable outcomes out of 6. P = 3/6 = 1/2. Hence the answer is 1/2.
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Q3 EasyFrom 100 lottery tickets 5 are winners. One ticket is drawn at random. What is the probability of winning?ExplanationP(E) = favourable / total. Favourable = 5, total = 100. P = 5/100 = 1/20. Hence the answer is 1/20.
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Q4 EasyA spinner has 8 equal sections of which 3 are green. What is the probability of landing on green?ExplanationP(E) = favourable / total. Favourable green sections = 3, total = 8. P = 3/8. Hence the answer is 3/8.
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Q5 EasyOne card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?ExplanationP(E) = favourable / total. Face cards are J, Q, K → 3 ranks × 4 suits = 12. Total = 52. P = 12/52 = 3/13. Hence the answer is 3/13.
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Q6 EasyA class of 12 students has 4 who wear glasses. One student is picked at random. What is the probability that the student wears glasses?ExplanationP(E) = favourable / total. Favourable = 4, total = 12. P = 4/12 = 1/3. Hence the answer is 1/3.
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Q7 EasyAn urn has 5 white and 2 black balls. One ball is drawn. What is the probability of drawing a black ball?ExplanationP(E) = favourable / total. Favourable black = 2, total = 7. P = 2/7. Hence the answer is 2/7.
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Q8 MediumTickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?ExplanationP(E) = favourable / total. Total tickets = 20. Multiples of 3: 3, 6, 9, 12, 15, 18 (6). Multiples of 5: 5, 10, 15, 20 (4). Common (15): 1. Favourable = 6 + 4 − 1 = 9. P = 9/20. Hence the answer is 9/20.
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Q9 MediumIn a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?ExplanationP(E) = favourable / total. Total = 8 + 7 + 6 = 21. Neither red nor green means blue → 7 favourable. P = 7/21 = 1/3. Hence the answer is 1/3.
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Q10 MediumA box has 6 apples and 4 oranges. One fruit is picked at random. What is the probability that it is not an apple?ExplanationP(E) = favourable / total. Not apple means orange → 4 favourable out of 10. P = 4/10 = 2/5. Hence the answer is 2/5.
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Q11 Medium50 balls include 10 red, 15 blue and 25 green. One ball is drawn. What is the probability that it is blue?ExplanationP(E) = favourable / total. Favourable blue = 15, total = 50. P = 15/50 = 3/10. Hence the answer is 3/10.
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Q12 HardA bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?ExplanationP(E) = favourable / total. Total balls = 7. Ways to draw 2 from 7 = 7C2 = 21. Non-blue balls = 5; ways = 5C2 = 10. P = 10/21. Hence the answer is 10/21.
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Q13 HardA speaks truth in 75% of cases and B in 80% of cases. Probability that they contradict each other describing the same event is:ExplanationP(E) uses independent cases. P(A true) = 3/4, P(A false) = 1/4; P(B true) = 4/5, P(B false) = 1/5. They contradict if (A true, B false) or (A false, B true): (3/4)×(1/5) + (1/4)×(4/5) = 3/20 + 4/20 = 7/20. Hence the answer is 7/20.
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Q14 HardFrom a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?ExplanationP(E) = favourable / total. Ways to choose 2 cards from 52 = 52C2 = 1326. Ways to choose 2 kings from 4 = 4C2 = 6. P = 6/1326 = 1/221. Hence the answer is 1/221.
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DS1 Easy
What is the probability of drawing a red ball from a bag?
Statement IThe bag has 4 red and 6 blue balls.
Statement IIThere are 10 balls in total and each ball is equally likely to be drawn.
ExplanationStatement I alone: 4 red and 6 blue give total 10, so P(red) = 4/10 = 2/5. Statement II alone gives the total but not the number of red balls. Answer: A. -
DS2 Easy
What is the probability of getting an even number on one roll of a die?
Statement IA fair six-sided die is used.
Statement IIThe even outcomes on the die are 2, 4 and 6.
ExplanationStatement I alone does not list which faces are even. Statement II alone does not give the total number of faces. Together: favourable = 3, total = 6, P = 3/6 = 1/2. Both needed. Answer: C.
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DS3 Medium
For the probability of winning a lottery draw. What is that probability?
Statement I200 tickets are sold and 8 of them are winning tickets.
Statement IIExactly one ticket is drawn at random from the 200 tickets.
ExplanationStatement I alone lacks confirmation that one ticket is drawn at random. Statement II alone lacks the winning count. Together: P = 8/200 = 1/25. Both needed. Answer: C. -
DS4 Medium
For the probability of landing on green on a spinner. What is that probability?
Statement IThe spinner has 5 green sections out of 20 equal sections.
Statement IIAll sections of the spinner are equally likely.
ExplanationStatement I alone: favourable = 5, total = 20 equal sections, so P = 5/20 = 1/4. Statement II alone gives no counts. Answer: A.