A balanced coin is tossed 3 times. Let A = {a head is obtained} and B = {a tail is obtained}. Calculate the probability to get two heads.
0.375
0.3333
Both (a) and (b)
To calculate the probability of getting two heads when a balanced coin is tossed 3 times, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n = number of trials (3 in this case)
- k = number of successful outcomes (2 in this case)
- p = probability of success for each trial (0.5 for a balanced coin)
- (n choose k) = n! / (k!(n-k)!)
Plugging in the values:
P(X = 2) = (3 choose 2) * (0.5)^2 * (1-0.5)^(3-2)
= 3 * 0.25 * 0.5
= 0.375
Therefore, the probability of getting two heads when a balanced coin is tossed 3 times is 0.375. So, the correct answer is (a) 0.375.