A fair six-faced die, numbered 1 to 6, is thrown three times. What is the probability that the number 6 comes up exactly twice?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{5}{72}\)
Three throws give \(6\times6\times6=216\) equally likely outcomes. For exactly two sixes, choose which 2 throws show 6; the remaining throw must show one of the other 5 numbers.
Ways to choose the 2 throws showing 6 \(={}^{3}C_2=3\) (1st and 2nd, 1st and 3rd, 2nd and 3rd)
The other throw shows 1, 2, 3, 4 or 5: 5 ways
Favourable outcomes \(=3\times5=15\)
Probability \(\displaystyle =\frac{15}{216}=\frac{5}{72}\)