Question

10 Marbles Jar A jar contains 10 marbles numbered 1 to 10. Each marble is equally likely to be selected A = {1, 2, 3, 4, 5; B={1, 2, 6, 7) C= {4, 5, 6, 7} D= {6,7,8,9; Given the events above, calculate the following probabilities. P(A)= P(B)= 2 P(C)= P(D) 3 P(A and B) = P( A and C)= 4 P(A and C)= P( B and C)- 5 P(A/B) = P(AC)= 6 P(AD)= P( BC) = 7 Determine if A and B are mutually exclusive 8 Determine if A and D are mutually exclusive Determine if A and D are independent 10 Determine if A and C are independent

Answer 1

0.5 (1) P(A) = 5 10 P(6) = 4 0,4 lo (2) PLC) 4 10 0.4 P(D) - 4 0.4 10 (3) P(A and B) = 0-2 P (A and C) V lo 22 2 / 0.2 (4) P(A and C) = = 0.2 P(B and c) = 2 10 = 0.2 10 0.2 (5) PLAIB) - PA and B) PB) 0.4 Os PLAIB) PL Alc) - P/A and C) P(c) P(A/C) = 0.5 0.2 0.4

16) PLAID) = 6/A and D) P(D) 0,4 PIAD) - o p(Blc) p(8 and o) Plo) 0.2 0.5 0.4 P(B/C) = 0.5 (7) P(A and B) = -0.2 #0 lo ..A and Bare not mutually exclusive 0 (8) P (A ands) ...A and I are mutually exclusive (9) PLA and D) = 0 P(A) P(D) 0.5x0.4 - 0.20 .P (A and D) & P(A) PLD) :. A and D are not independent

110 P/A and C) = 0.2 de P(A) P(c) - 0,5 Xo. 4 0.2 PIA and C) = P(A) PLC) independent and C are