A fair coin is tossed six times in a row. What is the probability that heads turns up in exactly four of the six tosses?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{15}{64}\)
Each toss of a fair coin gives H or T, so \(n\) tosses give \(2^n\) equally likely outcomes. The outcomes with exactly four heads are found by choosing which 4 of the 6 tosses show heads.
Total outcomes \(=2^6=64\)
Ways to choose the 4 tosses showing heads \(\displaystyle ={}^{6}C_4={}^{6}C_2=\frac{6\times5}{2}=15\)
Probability \(\displaystyle =\frac{15}{64}\)