Question

A student throws 3 coins in the air. Find the probability that exactly 1 lands on heads, given that at least 1 lands on tails.

A. 3/8
B. 3/7
C. 1/2
D. 3/4

Answer 1

To find the probability that exactly 1 coin lands on heads given that at least 1 coin lands on tails, we need to consider two different scenarios: 1) If exactly 1 coin lands on heads and 2 coins land on tails. 2) If exactly 2 coins land on heads and 1 coin lands on tails. The probability that exactly 1 coin lands on heads, given that at least 1 coin lands on tails, is 3/4.

Step-by-step explanation:

To find the probability that exactly 1 coin lands on heads given that at least 1 coin lands on tails, we need to consider two different scenarios:

1. If exactly 1 coin lands on heads and 2 coins land on tails.
2. If exactly 2 coins land on heads and 1 coin lands on tails.

Let's calculate the probability for each scenario:

1. Probability of exactly 1 coin landing on heads and 2 coins landing on tails:
   There are 3 ways in which exactly 1 coin can land on heads - HHT, HTH, and THH (where H represents heads and T represents tails). Each of these outcomes has a probability of (1/2)*(1/2)*(1/2) = 1/8. Therefore, the probability for this scenario is 3*(1/8) = 3/8.
2. Probability of exactly 2 coins landing on heads and 1 coin landing on tails:
   Similarly, there are 3 ways in which exactly 2 coins can land on heads - HHT, HTH, and THH. Each of these outcomes has a probability of (1/2)*(1/2)*(1/2) = 1/8. Therefore, the probability for this scenario is 3*(1/8) = 3/8.

Finally, we add the probabilities from both scenarios to get the total probability that at least 1 coin lands on tails: (3/8) + (3/8) = 6/8 = 3/4.

Therefore, the probability that exactly 1 coin lands on heads, given that at least 1 coin lands on tails, is 3/4.