A coin is tossed 5 times, the probability of getting at least 3 heads is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{1}{2} \)
Let X be the number of heads in 5 tosses. X is binomial with n = 5 and p = 1/2, so each of the \( 2^5=32 \) outcomes is equally likely.
\( \displaystyle P(X\ge 3)=\frac{{}^{5}C_3+{}^{5}C_4+{}^{5}C_5}{2^5} \)
\( \displaystyle =\frac{10+5+1}{32} \)
\( \displaystyle =\frac{1}{2} \)
Shortcut: With 5 tosses, “at least 3 heads” and “at least 3 tails” cover every outcome with no overlap, and by symmetry they are equally likely. So each has probability 1/2.