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Joint Entrance Examination
Mathematics
Probability
Question 192
Question 192 of 417
Medium
MCQ
A fair die tossed until 6 appears;
X
X
X
=tosses required. Find
P
(
X
≥
5
∣
X
>
2
)
P(X\ge5\mid X>2)
P
(
X
≥
5
∣
X
>
2
)
.
A
125
/
216
125/216
125/216
B
11
/
36
11/36
11/36
C
5
/
6
5/6
5/6
D
25
/
36
25/36
25/36
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Official solution
By the memoryless property of the geometric distribution, \[P(X\ge5\mid X>2) = P(X\ge3) = \left(\frac56\right)^2 = \frac{25}{36}\]
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