Maths - Ans.fyi 參考答案

Maths

2010-01-07 4:23 am

1.There are 6MC question in a short Quiz and 5 options are given for each question.2 marks are awarded for a correct answer and 1 mark is deducted for a wrong answer.If a student answers the questions by guessing,find the probility that

a.his total sore is negative;
b.his total sore is zero;
c.his total sore is positive.

2.a .Airlines find that each passenger who reserves a seat fails to turn up with probability 0.1 independently of the other passengers.So Airlines ABC always sell 15 tickets for their 14 seat airplane while Airways XYZ always sell 3 tickets for their 28 seat airplane. which is more often overbooked?(Please clearly show your supporting figures).

b.In a shipment of 200 televisions ,3 are defective. If a person buys two televisions,what is the probability that both are working properly?
(correct answer to 4d.p)

回答 (1)

用戶9112

2010-01-07 5:29 am

✔ 最佳答案

(1) The scores for different combinations of correct / wrong answers are:
6 correct : 6*2 = 12
5 correct : 5*2 - 1 = 9
4 correct : 4*2 - 2 = 6
3 correct : 3*2 - 3 = 3
2 correct : 2*2 - 4 = 0
1 correct : 1*2 - 5 = -3
0 correct : 0*2 - 6 = -6
(a) Probability of negative score = (6C0)(4/5)^6 + (6C1)(4/5)^5(1/5)
= 0.2621 + 0.3932
= 0.6554
(b) Probability to get zero score = (6C2)(4/5)^4*(1/5)^2 = 0.2458
(c) Probability to get positive score = 1 - 0.6554 - 0.2458 = 0.0989
(2)(a) Probability for airline ABC for overbooking, i.e. all 15 passengers show up
= (15C15)(0.9)^15(0.1)^0
= 0.2059
Probability for airline XYZ for overbooking, i.e. all 30 or 29 passengers show up
= (30C30)(0.9)^30(0.1)^0 + (30C29)(0.9)^29(0.1)^1
= 0.0424 + 0.1413
= 0.1837
Airline ABC is more often overbooked
(b) Probability of defective unit = 3/200 = 0.015
Probability of 2 sets working properly = (1 - 0.015)^2 = 0.9702

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