14. Suppose you select three cards from an ordinary playing deck of 52 cards. De

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14. Suppose you select three cards from an ordinary playing deck of 52 cards. Define the following events: A: Event A occurs when all three selected cards are of the suit "Hearts B: Event B occurs when at least one card has a value of 10 (10J,Q,K) C: Event C occurs when the sum of the face value of the three cards equals 30 (an ace has a value of 11). a. Which (if any) of the pairwise events (A-B).(A-C) or(B-C) are independent? Prove your answer Which (if any) of the pairwise events (A-B),(A-C) or(B-C) are dependent? Prove your answer b. All three pairwise events are dependent. First compute: P 0.01 2941; P(B)-1- 0.67692. To compute the probability of C, note first that we can obtain a sum of 30 in the following way: 10/10/10, A/A/8, and A/10/9. There are (39) ways to obtain a 10/10/1o4 (2) ways to obtain an A/A/8 and 4*16*4 ways to obtain an A/10/9. Therefore, P(C)- 0.038009 ,22000 0.00914; PAnG+ Furthermore, P(AnB) 0. 0000452489; P(BnC) 22,100 3 161 4-16+4 = 0.036923. PLAI B)=( 0.00914)/(0.67692):001350233 z P(A) and therefore A and B are dependent. P(AIC)-( 0.0000452489)/(0.038009)-0.00119024 P(A) and therefore A and Care dependent. P(BIC-0.036923)/(0.038009)-0.6666x P(B) and therefore B and C are

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