Probability_4－航空百大

標題:

Probability

發問:

1. Two events A and B are such that P(a)= 8/15, P(b)=1/3, P(alb)=1/5(a) find the prob. that both events occur(b) find the prob. that only one of the two events occurs(c) find the prob. that neither event occurs2. Events C and D are such that P(c) =4/7, P(C and D^,)=1/3, P(cld) = 5/14(a)findP(c and... 顯示更多 1. Two events A and B are such that P(a)= 8/15, P(b)=1/3, P(alb)=1/5 (a) find the prob. that both events occur (b) find the prob. that only one of the two events occurs (c) find the prob. that neither event occurs 2. Events C and D are such that P(c) =4/7, P(C and D^,)=1/3, P(cld) = 5/14 (a)findP(c and D) (b)find P(D) (C) find P(dlc)

最佳解答:

1. (a) The required probability is P(A and B) = P(A|B) P(B) = (1/5)(1/3) = 1/15 (b) Consider P(A or B) = P(A) + P(B) - P(A and B) = 8/15 + 1/3 - 1/15 = 12/15 The required probability is P(A or B) - P(A and B) = 12/15 - 1/15 = 11/15 (c) The required probability is 1 - P(A or B) = 1 - 12/15 = 3/15 = 1/5 圖片參考：https://s.yimg.com/rk/HA00430218/o/1095997353.png 2. (a) Since P(C) = P(C and D) + P(C and D'), then P(C and D) = P(C) - P(C and D') = 4/7 - 1/3 = 5/21 (b) Since P(C|D) = P(C and D)/P(D), then P(D) = P(C and D) / P(C|D) = (5/21) / (5/14) = 14/21 = 2/3 (c) P(D|C) = P(D and C) / P(C) = (5/21) / (4/7) = (5/21) (7/4) = 5/12

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其他解答:

1. (a) The required probability is P(A and B) = P(A|B) P(B) = (1/5)(1/3) = 1/15 (b) Consider P(A or B) = P(A) + P(B) - P(A and B) = 8/15 + 1/3 - 1/15 = 12/15 The required probability is P(A or B) - P(A and B) = 12/15 - 1/15 = 11/15 (c) The required probability is 1 - P(A or B) = 1 - 12/15 = 3/15 = 1/5 2. (a) Since P(C) = P(C and D) + P(C and D'), then P(C and D) = P(C) - P(C and D') = 4/7 - 1/3 = 5/21 (b) Since P(C|D) = P(C and D)/P(D), then P(D) = P(C and D) / P(C|D) = (5/21) / (5/14) = 14/21 = 2/3 (c) P(D|C) = P(D and C) / P(C) = (5/21) / (4/7) = (5/21) (7/4) = 5/12 1. Two events A and B are such that P(a)= 8/15, P(b)=1/3, P(alb)=1/5 (a) find the prob. that both events occur (b) find the prob. that only one of the two events occurs (c) find the prob. that neither event occurs 2. Events C and D are such that P(c) =4/7, P(C and D^,)=1/3, P(cld) = 5/14 (a)findP(c and D) (b)find P(D) (C) find P(dlc)