A fair coin is flipped four times in a row. Find the chance that heads turns up in exactly two of the four flips.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{3}{8}\)
Each flip of a fair coin gives H or T, so \(n\) flips give \(2^n\) equally likely outcomes. The outcomes with exactly two heads are found by choosing which 2 of the 4 flips show heads.
Total outcomes \(=2^4=16\)
Ways to choose the 2 flips showing heads \(\displaystyle ={}^{4}C_2=\frac{4\times3}{2}=6\)
These are HHTT, HTHT, HTTH, THHT, THTH, TTHH
Probability \(\displaystyle =\frac{6}{16}=\frac{3}{8}\)