A pair of dice is thrown. If the two numbers appearing on them are different then the probability that the sum of the number is 6, is.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{2}{15} \)
Let F be the event that the two numbers are different and E the event that the sum is 6. Of the 36 outcomes, 6 have equal numbers, so n(F) = 30.
The outcomes of F with sum 6 are (1, 5), (5, 1), (2, 4), (4, 2), so \( n(E\cap F)=4 \).
By conditional probability,
\( \displaystyle P(E|F)=\frac{n(E\cap F)}{n(F)} \)
\( \displaystyle =\frac{4}{30}=\frac{2}{15} \)
Tip: (3, 3) has sum 6 but its numbers are equal, so it is not in F. Counting it gives \( \frac{5}{30}=\frac{1}{6} \), which is Option (2).