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S1 probability help on Q.

How do I attempt this q.
The probability that Ajita gets up before 6.30 am in the morning is 0.7
The probability that she goes for a run in the morning is 0.35
The probability that Ajita gets up after 6.30 am and does not go for a run is 0.22
Let A represent the event that Ajita gets up before 6.30 am and B represent the event that she
goes for a run in the morning.
Find
(a) P(A ∪ B), (2 marks)
(b) P(A ∩ B′), (2 marks)
(c) P(B | A). (3 marks)
(d) State, with a reason, whether or not events A and B are independent. (2 marks)


I have no idea on where to start, :colondollar:
thanks :smile:
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by Hi, How are you ?

I have no idea on where to start


I drew a Venn Diagram
Reply 2
Avatar for Notnek
Notnek
21
Original post by Hi, How are you ?
How do I attempt this q.
The probability that Ajita gets up before 6.30 am in the morning is 0.7
The probability that she goes for a run in the morning is 0.35
The probability that Ajita gets up after 6.30 am and does not go for a run is 0.22
Let A represent the event that Ajita gets up before 6.30 am and B represent the event that she
goes for a run in the morning.
Find
(a) P(A ∪ B), (2 marks)
(b) P(A ∩ B′), (2 marks)
(c) P(B | A). (3 marks)
(d) State, with a reason, whether or not events A and B are independent. (2 marks)


I have no idea on where to start, :colondollar:
thanks :smile:

Try drawing a Venn Diagram with two circles representing A and B.

P(not A and not B) = 0.22 so the number 0.22 will go outside the circles.

If you're still stuck, post what numbers you've managed to write in the diagram.
(edited 11 years ago)
Original post by notnek
Try drawing a Venn Diagram with two circles representing A and B.

P(not A and not B) = 0.22 so the number 0.22 will go outside the circles.

If you're still stuck, post what numbers you've managed to write in the diagram.


Hi, so for A, i drew a diagram and so i done 1-0.22 = 0.78.
b, 0.43
c, 0.386 (3sf)
d, not indp. as P(anb) does not equal P(a) * P(b), i.e. 0.27 does not equal 0.105
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by Hi, How are you ?
Hi, so for A, i drew a diagram and so i done 1-0.22 = 0.78.
b, 0.43
c, 0.386 (3sf)
d, not indp. as P(anb) does not equal P(a) * P(b), i.e. 0.27 does not equal 0.105


All looks good
Reply 5
Avatar for Notnek
Notnek
21
Original post by Hi, How are you ?
Hi, so for A, i drew a diagram and so i done 1-0.22 = 0.78.
b, 0.43
c, 0.386 (3sf)
d, not indp. as P(anb) does not equal P(a) * P(b), i.e. 0.27 does not equal 0.105

Slightly faster method for d):

For independent events A and B, P(B|A) = P(B).

P(B|A) is your answer to c) and P(B) is given in the question.
Original post by notnek
Slightly faster method for d):

For independent events A and B, P(B|A) = P(B).

P(B|A) is your answer to c) and P(B) is given in the question.


Thanks :biggrin:

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