Four fair coins are tossed once. Calculate the probability of having equal heads and tails....
FURTHER MATHEMATICS
WAEC 2015
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: B. \(\frac{3}{8}\)
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 = \(6p^{2}q^{2} = 6(\frac{1}{2}^{2})(\frac{1}{2}^{2})\)
= \(\frac{6}{16} = \frac{3}{8}\).
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