Question

a bag contains three indistinguishable coins with the following properties: one coin has a 30% chance to land on heads, another has a 60% chance to land on heads, the last one has a 80% chance to land on heads. we randomly draw a coin out of the bag and flip it. suppose it lands on heads, what is the probability it lands on heads again on a reflip?

Answer 1

To find the probability that the coin lands on heads again on a reflip, we need to calculate the conditional probability by considering the initial probability of selecting each coin from the bag and the probability of flipping heads with that coin. The result is 88.89%.

Step-by-step explanation:

To determine the probability that a coin lands on heads again on a reflip, we need to consider the initial probability of selecting each coin from the bag and the probability of flipping heads with that coin. Let's calculate the conditional probability:

Step 1:

Calculate the probability of selecting each coin from the bag:

Probability of selecting the first coin: 1/3

Probability of selecting the second coin: 1/3

Probability of selecting the third coin: 1/3

Step 2:

Now, calculate the probability of flipping heads with each coin:

Probability of flipping heads with the first coin: 30%

Probability of flipping heads with the second coin: 60%

Probability of flipping heads with the third coin: 80%

Step 3:

Apply the law of total probability to calculate the overall probability:

[Probability of selecting the first coin and flipping heads] + [Probability of selecting the second coin and flipping heads] + [Probability of selecting the third coin and flipping heads]

(1/3)*(0.3) + (1/3)*(0.6) + (1/3)*(0.8) = 0.9

Step 4:

Finally, divide the probability of selecting and flipping heads with the third coin by the overall probability:

(1/3)*(0.8) / 0.9 = 0.8889

Therefore, the probability that the coin lands on heads again on a reflip is 88.89%.