Question
Mathematics Question on Conditional Probability
If two unbiased six-faced dice are thrown simultaneously until a sum of either 7 or 11 occurs, then the probability that 7 comes before 11 is
A
41
B
43
C
95
D
185
Answer
43
Explanation
Solution
Let A be the event of obtained sum of 7 and B be the event of obtained sum of 11.
∴n(A)=(2,5),(5,2),(3,4),(4,3),(1,1),(6,1)=6
Now, P(A)=366=61
and n(B)=(5,6),(6,5)=2
∴P(B)=362=181
C= Neither a sum of 11 nor a sum of 7 shows of
∴P(C)=3636−(6+2)
=3636−8=3628=97
Required probability (p)
=366+366×3628+(3628)2(366)+(3628)3(366)…
=61[1−971]
=61×29=43