Coins of 1, 2 and 5 rupees are tossed. What is the probability of getting…
2023
Coins of 1, 2 and 5 rupees are tossed. What is the probability of getting heads on a 1-rupee coin, tails on a 2-rupee coin and heads on a 5-rupee coin?
- A.
1/2
- B.
1/4
- C.
1/8
- D.
1/16
Show answer & explanation
Correct answer: C
Concept: When several events are independent of one another, the probability that all of them occur together (jointly) equals the product of their individual probabilities: P(A and B and C) = P(A) x P(B) x P(C).
Application: Each coin toss is a fair, independent trial with exactly two equally likely outcomes (Head or Tail), so the probability of any one specified outcome on a single coin is 1/2. For the three coins in this question:
P(Head on the 1-rupee coin) = 1/2
P(Tail on the 2-rupee coin) = 1/2
P(Head on the 5-rupee coin) = 1/2
Since the three tosses are independent, multiply these probabilities together: 1/2 x 1/2 x 1/2 = 1/8.
Cross-check: Listing every equally likely outcome for three coins gives 23 = 8 total possibilities (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT, in the order 1-rupee, 2-rupee, 5-rupee coin). Exactly one of these, HTH, matches the required outcome (Head, Tail, Head), so the probability is 1/8 - confirming the result above.
