Four fair coins are tossed once. Calculate the probability of having equal heads and tails.
-
A.
(frac{1}{4}) -
B.
(frac{3}{8}) -
C.
(frac{1}{2}) -
D.
(frac{15}{16})
Correct Answer: Option B
Explanation
Let (p(head) = p = frac{1}{2}) and (p(tail) = q = frac{1}{2})
((p + q)^{4} = p^{4} + 4p^{3}q + 6p^{2}q^{2} + 4pq^{3} + q^{4})
The probability of equal heads and tails = (6p^{2}q^{2} = 6(frac{1}{2}^{2})(frac{1}{2}^{2}))
= (frac{6}{16} = frac{3}{8}).