A dice is thrown three times. If the first throw shows 4, then the probability of getting 15 as the sum is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{18}\)
The first throw is already known to be 4, so only the last two throws are left to chance. They must make up the rest of the sum.
The other two throws must add up to \(15-4=11\)
Pairs giving 11: (5, 6) and (6, 5), that is, 2 favourable outcomes
Outcomes of two throws: \(6\times6=36\)
Probability \(\displaystyle =\frac{2}{36}=\frac{1}{18}\)
Tip: “If the first throw shows 4” makes the 4 a given fact. Counting all \(6^{3}=216\) outcomes of three throws gives \(\frac{2}{216}=\frac{1}{108}\), which is the probability that the first throw is 4 and the sum is 15 — a different question.