1 point If PA02 PB 01 and PAU B 028 then PAn B a Are even

(1 point) If P(A)-0.2, P(B) = 0.1, and P(AU B) = 0.28, then P(An B) = (a) Are events A and B independent? (enter YES or NO) (b) Are A and B mutually exclusive? (enter YES or NO)

Solution

Pa = 0.2
Pb = 0.1
P(aub) = 0.28

We can find P(aub) = Pa + PB - P(anb)
So, P(anb) = 0.2 + 0.1 - 0.28 ----> 0.02

a)Independent :
For independent
P(anb) = P(a) * P(b)

P(a) * p(b) comes out to :

0.2 * 0.1

0.02

But P(anb) is also 0.02

So, yep!

Independent!

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b)
Mutually exclusive :

For mult exclusive
P(aub) = P(a) + P(b)

0.28 = 0.2 + 0.1

Not true

So, not mutually exclusive!