Question 1

A fair coin is tossed 3 times. What is the probability of getting at least one head?

Accepted Answer

Step 1: Total possible outcomes when tossing a coin 3 times = 2³ = 8. Step 2: Outcomes with at least one head = Total outcomes - Outcomes with no heads (all tails). Step 3: Outcomes with all tails = 1 (TTT). Step 4: Outcomes with at least one head = 8 - 1 = 7. Step 5: Probability = 7/8.

Question 2

A bag contains 5 red balls, 7 blue balls, and 8 green balls. If one ball is drawn at random, what is the probability that it is neither red nor green?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Step 2: Balls that are neither red nor green = blue balls = 7. Step 3: Probability = 7/20.

Question 3

A number is chosen at random from the set {1, 2, 3, ..., 50}. What is the probability that the number is divisible by 3 or divisible by 5?

Accepted Answer

Step 1: Total numbers = 50. Step 2: Numbers divisible by 3: ⌊50/3⌋ = 16 (3, 6, 9, ..., 48). Step 3: Numbers divisible by 5: ⌊50/5⌋ = 10 (5, 10, 15, ..., 50). Step 4: Numbers divisible by both 3 and 5 (i.e., by 15): ⌊50/15⌋ = 3 (15, 30, 45). Step 5: Using inclusion-exclusion: 16 + 10 - 3 = 23. Step 6: Probability = 23/50.

Question 4

A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously without replacement. What is the probability that both balls are of different colours?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Total ways to draw 2 balls = C(20,2) = 190. Step 2: Ways to draw 2 balls of same colour = C(5,2) + C(7,2) + C(8,2) = 10 + 21 + 28 = 59. Step 3: Ways to draw 2 balls of different colours = 190 - 59 = 131. Step 4: Probability = 131/190.

Question 5

A fair coin is tossed 5 times. What is the probability of getting at least 2 heads but not more than 4 heads?

Accepted Answer

Step 1: Total outcomes = 2^5 = 32. Step 2: We need P(2 ≤ H ≤ 4) where H is number of heads. Step 3: P(H=2) = C(5,2)/32 = 10/32. P(H=3) = C(5,3)/32 = 10/32. P(H=4) = C(5,4)/32 = 5/32. Step 4: P(2 ≤ H ≤ 4) = (10 + 10 + 5)/32 = 25/32.

Question 6

Three cards are drawn without replacement from a standard deck of 52 cards. What is the probability that all three cards are face cards (Jack, Queen, or King)?

Accepted Answer

Step 1: Total face cards = 12 (Jack, Queen, King in each of 4 suits). Step 2: Total ways to draw 3 cards from 52 = C(52,3) = 22,100. Step 3: Ways to draw 3 face cards from 12 = C(12,3) = 220. Step 4: Probability = 220/22,100 = 11/1,105.

SSC GD Constable Probability

SSC GD Constable Probability — Past Exam Questions

Probability— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Probability