Question

a coin is biased so that the head is 3 times as likely to occur as tail. if the coin is tossed twice, then the expected value of the number of tails is

Answer 1

To find the expected value of the number of tails when a biased coin is tossed twice, we need to calculate the probabilities of each possible outcome and multiply them by the number of tails in each outcome. The expected value is the sum of these calculations, and in this case, it is 1/2.

Step-by-step explanation:

To find the expected value of the number of tails when a biased coin is tossed twice, we need to calculate the probability of each possible outcome and then multiply it by the number of tails in that outcome. In this case, the coin is biased, and the probability of getting a head (H) is 3 times the probability of getting a tail (T).

Let's calculate the probabilities:

• Probability of getting two heads: (3/4) x (3/4) = 9/16
• Probability of getting one head and one tail: (3/4) x (1/4) + (1/4) x (3/4) = 6/16
• Probability of getting two tails: (1/4) x (1/4) = 1/16

Now, let's calculate the expected value:
Expected value = (Number of tails in each outcome) x (Probability of each outcome)

Expected value = (0 x 9/16) + (1 x 6/16) + (2 x 1/16) = 0 + 6/16 + 2/16 = 8/16 = 1/2

Therefore, the expected value of the number of tails is 1/2.