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Joint Entrance Examination
Mathematics
Probability
Question 120
Question 120 of 417
Medium
MCQ
Ajay will not appear in the JEE exam with probability
p
=
2
7
p=\dfrac27
p
=
7
2
, while both Ajay and Vijay will appear with probability
q
=
1
5
q=\dfrac15
q
=
5
1
. Then the probability that Ajay will appear and Vijay will not appear is:
A
9
/
35
9/35
9/35
B
18
/
35
18/35
18/35
C
24
/
35
24/35
24/35
D
3
/
35
3/35
3/35
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Official solution
P
(
Ajay appears
)
=
1
−
2
7
=
5
7
P(\text{Ajay appears}) = 1-\dfrac27=\dfrac57
P
(
Ajay appears
)
=
1
−
7
2
=
7
5
. \[P(\text{Ajay appears, Vijay does not}) = P(\text{Ajay appears})-P(\text{both appear}) = \frac57-\frac15 = \frac{25-7}{35}=\frac{18}{35}\]
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