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S1 probability help on Q. Watch

1. 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,
thanks
2. (Original post by Hi, How are you ?)
I have no idea on where to start
I drew a Venn Diagram
3. (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,
thanks
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.
4. (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
5. (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
6. (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.
7. (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

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