4.) A random sample of 396 students were recent surveyed regarding their class standing (freshman, sophomore, junior, senior) and their major type (STEM vs. Non-STEM). The following contingency table gives the two-way classification of the responses. Freshman Sophomore Junior Senior 20 48 18 78 85 56 60 31 Suppose one student is randomly selected from the group. Calculate the following probabilities. Round solutions to three decimal places, if necessary. P(STEM)= P(Sophomore)= PSophomore | Non-STEM) = PSophmore and Non-STEM) = Are the events "Sophomore" and "Non-STEM" indpendent or dependent? PSophmore or Non-STEM) = STEM Non-STEM 5.) Use the given information to address the prompts below. P(A)=0.25 P(B)=0.44 P(A/B)=0.28 Round solutions to three decimal places, if necessary. Determine if A and B are independent or dependent events. Determine P(A and B). P(A and B) = Determine if A and B are mutually exclusive or mutually non-exclusive events. Determine P (A or B). P(A or B) = 6.) If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a Spade or Heart? Round the solution to four decimal places, if necessary. P(Spade or Heart) = +4 2+ + + 14 ++ + +4 69 C C 5A . Me Ma 14 N ON N 2+ N . 244 23