wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let A,B and C be three events, which are pair-wise independent and ¯¯¯¯E denotes the complement of an event E. If P(ABC)=0, then P[(¯¯¯¯A¯¯¯¯B)|C] is equal to:

A
P(¯¯¯¯A)P(B)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
P(¯¯¯¯A)P(¯¯¯¯B)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
P(¯¯¯¯A)+P(¯¯¯¯B)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
P(A)+P(¯¯¯¯B)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A P(¯¯¯¯A)P(B)
P[(¯¯¯¯A¯¯¯¯B)|C]=P(¯¯¯¯A ¯¯¯¯B) C)P(C)=P((AB)C)P(C)=P(C)P((AB)C)P(C) [P(AB)=P(A)P(AB)]=P(C)[P(AB)+P(C)P(ABC)]P(C)=P(C)[P(A)+P(B)P(AB)+P(C)P(ABC)]P(C)=P(C)[P(AC)+P(BC)P(ABC)]P(C)=P(C)P(A)P(C)P(B)P(C)P(C)=1P(A)P(B)=P(¯¯¯¯A)P(B) or P(¯¯¯¯B)P(A)

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Events
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon