Given events E, F where Pr(E) = 0.32, Pr(F) = 0.28, and Pr(F ∩ E′) = 0.23,
find the following probabilities.

(a) E ∩ F
(b) E ∩ F′
(c) E′ ∩ F′

Question

Given events E, F where Pr(E) = 0.32, Pr(F) = 0.28, and Pr(F ∩ E′) = 0.23,
find the following probabilities.

(a)	 E ∩ F
(b)	 E ∩ F′
(c)	 E′ ∩ F′

anonymous · Answer

|dw:1381545517568:dw|

anonymous · Answer

a venn diagram is a good place to start
i filled in $P(F\cap E')$ now we can fill in the rest

anonymous · Answer

since $P(F)=.28$ and well already have accounted for $.23$ that means all that is left for the intersection is  $.05$|dw:1381545662572:dw|

anonymous · Answer

now we have $.05$ also in $E$ and we know $P(E)=.32$ we can find the rest of $E$ as $.32-.05=.27$|dw:1381545764660:dw|

anonymous · Answer

i got them all except c

anonymous · Answer

now for the outside stuff, since the total has to be 1 and we have accounted for $.55$ that leaves $.45$ outside |dw:1381545860198:dw|