Question

Three coins are tossed. two of them are fair and one is biased so that a head is three times as likely as a tail. find the probability of getting two heads and a tail.

O 7/16
O ¾
O 9/16
O 1/2

Answer 1

To find the probability of getting two heads and one tail with two fair coins and one biased coin, we calculate the probability of each such event separately and sum them up, resulting in a total probability of 7/16.

option a is the correct

Step-by-step explanation:

The question requires finding the probability of getting two heads and one tail when three coins are tossed, where two are fair and one is biased (with heads being three times as likely as tails). To solve this, we start by determining the probability of each outcome for the biased coin, which are P(Head) = 3/4 and P(Tail) = 1/4. For the fair coins, each outcome has a probability of 1/2. We can now calculate the combined probability:

• Probability of getting two heads (one from each fair coin) and one tail (from the biased coin): (1/2 * 1/2 * 1/4) = 1/16.
• Probability of getting one head (from the biased coin) and one head and one tail (from the fair coins): (3/4 * 1/2 * 1/2) = 3/16.
• Probability of getting one head (from the first fair coin), one tail (from the second fair coin), and one head (from the biased coin): (1/2 * 1/2 * 3/4) = 3/16.

Adding these probabilities together gives us the total probability of the desired outcome: 1/16 + 3/16 + 3/16 = 7/16.