A coin is weighted in such a way that a tail is twice as likely to occur as a head. If the coin is tossed twice, what is the probability of obtaining two tails?
2/3 * 2/3 = ?
0.4
no solution
To find the probability of obtaining two tails, we need to first determine the specific probabilities of obtaining a head and a tail.
Let's assign the probability of obtaining a head as H and the probability of obtaining a tail as T. We are given that the probability of obtaining a tail is twice as likely as obtaining a head. Therefore, we can represent this as:
T = 2H
Since the sum of all probabilities must equal 1, we can write:
H + T = 1
Now, substitute the value of T from the first equation into the second equation:
H + 2H = 1
Combine like terms:
3H = 1
Solve for H:
H = 1/3
Now, substitute the value of H back into the first equation to find T:
T = 2(1/3) = 2/3
So, the probability of obtaining a head is 1/3, and the probability of obtaining a tail is 2/3.
To find the probability of obtaining two tails when the coin is tossed twice, we need to multiply the probabilities of obtaining a tail on each toss:
Probability of two tails = (Probability of obtaining a tail on first toss) x (Probability of obtaining a tail on second toss)
= T x T
= (2/3) x (2/3)
= 4/9
Therefore, the probability of obtaining two tails when the coin is tossed twice is 4/9, or approximately 0.4444.