7. Events E and F are mutually exclusive events. Given the Venn Diagram to the right, indicate the following probabilities: a) P (E ? F) ? b) P (E ? F) ? c) P ( E? ) ? d) P ( E ? F )? ? P(E) = 0.1 and P(F) = 0.5 E 0.1 F 0.5 0.4 8. Conditional probability. Given the probabilities of Event E and Event F and their intersection in the two cases below, fill in the blank boxes with the appropriate probability numbers for each region of the Venn Diagram, and then calculate the conditional probability of P ( F | E ) for each case.
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a) P(E ∩ F) = 0 because E and F are mutually exclusive events, which means they cannot occur at the same time. b) P(E ∪ F) = P(E) + P(F) - P(E ∩ F) = 0.1 + 0.5 - 0 = 0.6 c) P(E') = 1 - P(E) = 1 - 0.1 = 0.9 d) P((E ∪ F)') = 1 - P(E ∪ F) = 1 - 0.6 = 0.4 Show more…
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$$ \begin{aligned} &\text { Consider the following Venn diagram, where }\\ &P\left(E_{1}\right)=.2, P\left(E_{2}\right)=P\left(E_{3}\right)=.04, P\left(E_{4}\right)=.06\\ &P\left(E_{5}\right)=.08, P\left(E_{6}\right)=.15, P\left(E_{7}\right)=.25, \text { and }\\ &P\left(F_{0}\right)=18 \end{aligned} $$ Find the following probabilities: a. $P\left(A^{c}\right)$ b. $P\left(B^{c}\right)$ c. $P\left(A \cap B^{c}\right)$ d. $P(A \cap B)$ e. $P(A \cup B)$ f. $P\left(A^{c} \cup B^{c}\right)$ g. Are events $A$ and $B$ mutually exclusive? Why?
9.) (10) The Venn diagram below represents probabilities for events A and B. Determine each probability. (a) P(A AND B) (b) P(A OR B) (c) P(NOT A AND NOT B) (d) P(A|B) (e) P(B|A)
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