Question

A die is thrown twice and found that the sum of the numbers is 6. Find the conditional probability of getting number 4 at least once.

Hint:

Restrict the sample space to the 5 outcomes summing to 6, then count how many contain a 4.

Answer 1

Step 1: Using the probability-ratio formula instead of counting shortcut:
\(P(F)=\dfrac{5}{36}\) (5 favourable pairs out of 36 total equally likely pairs). \(P(E\cap F)=\dfrac{2}{36}\) (the pairs \((2,4)\) and \((4,2)\), both giving sum 6 and containing a 4).

Step 2: Applying the conditional probability formula:
\(P(E/F)=\dfrac{P(E\cap F)}{P(F)}=\dfrac{2/36}{5/36}=\dfrac{2}{5}\).

Final Answer:
Same answer via the formula: \(\boxed{\dfrac{2}{5}}\).