2P(ace and heart) P(ace or heart) P(even number or Heart) 20 313 P(even number a

Question

2P(ace and heart) P(ace or heart) P(even number or Heart) 20 313 P(even number and Heart) 3 0 3. Se Assume we are in a assisted living facility. We wish to select an individual from the facility at random. Let P(A) be the probability of having arthritis and let P(B) be the probability of having dementia. For each of the following situation, find the missing value and determine whether each situation could occur. d 3(AUT) P(B) = .10 IN( P(A U B)-1.1 P(A)= .32 P(B) = .17 P(A n B) = .10 P(A U B) = b) P(A)= .87 PCB) = P(A n B) = .30 P(A U B) = .95 c) d) P(A) = .7 P(B) = .5 P(A n B) = .6 P(A U B) =

Explanation / Answer

a)P(A n B) =P(A)+P(B)-P(A U B) =0.32+0.10-1.1 =-0.68 (as any probability can not be greater than 1 or less than 0; this is not possible

b)P(A U B) =P(A)+P(B)-P(A n B) =0.32+0.17-0.10 =0.39

c)P(B) =P(A U B)+P(A n B) -P(A) =0.95+0.3-0.87=0.38

d) P(A U B)=P(A)+P(B) -P(A n B) =0.7+0.5-0.6=0.6 ( not possible as P(A n B) can not be greater than P(B))

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