A coin is loaded in such way that a tail is three times as likely to occur as a head. If the coin is flipped twice. Find the probability that two heads occur
To find the probability of two heads occurring when a coin is flipped twice, we need to first determine the probability of getting a head or a tail on a single flip.
Given that a tail is three times as likely as a head, let's assign probabilities to each outcome. Let P(H) represent the probability of getting a head and P(T) represent the probability of getting a tail.
Since a tail is three times more likely, we can set up the equation:
P(T) = 3P(H)
Now, let's find the sum of the probabilities:
P(H) + P(T) = 1
Substituting the value of P(T) from the previous equation, we get:
P(H) + 3P(H) = 1
4P(H) = 1
P(H) = 1/4
Therefore, the probability of getting a head is 1/4, and the probability of getting a tail is 3/4.
Now, to find the probability of two heads occurring in two flips, we need to multiply the individual probabilities together:
P(2 H) = P(H) × P(H) = (1/4) × (1/4) = 1/16
So, the probability of two heads occurring is 1/16.