You have a bag with two coins. one will come up heads 40% of the time, and the other will come up heads 60%. you pick a coin randomly, flip it and get a head. what is the probability it will be heads on the next flip?

13/50

Step-by-step explanation:

First, we need to put all the possible scenarios.

Let's call coin A as the coin that flips head 40% of the time, and coin B the 60% of the time.

Now, 40% in fraction is 40/100 = 4/10 = 2/5 for coin A. This is the probability of the coin A to get head. (Pa)

60% of the time is 60/100 = 6/10 = 3/5. Probability to get head in coin B (Pb)

Now, we don't know which coin is picked, all we know is that the first flipping is head. so, as the coins are picked randomly, we have 1/2 probability to choose either coin A or coin B, so, let's suppose we picked coin A:

Pa = 1/2 * 2/5 = 2/10 * 2/5 = 4/50

If the coin picked is coin B:

Pb = 1/2 * 3/5 = 3/10 * 3/5 = 9/50

So, finally the probability that if we flip the coin a second time, to get a head, no matter which coin was picked, is just the sum of both probabilities so:

P = 4/50 + 9/50 = 13/50

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step-by-step explanation:

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