[URGENT!!!] F.5 Probability (15 points)

2008-10-22 3:53 am

1.) In a basketball match, the Conqueror Team attempted 150 shots
in the whole match, and the three players A,B and C made up
42%,20% and 18% of the shots respectively.
Their soring rates are 3/7,7/10 and 5/9 respectively, and
the other players scored a total of 3 shots.

Find the scoring rate of the other players in Conqueror.

2.)Two cards are drawn in succession from a pack of 52 playing cards
without replacement.
Find the probability that the first card is red and the second card
is not a diamond.

3.) The three classes 5A,5B and 5C attend a quiz contest.
Three representatives from each class will answer 10 questions,
and every question has to be answered. If any representive answers a
question correctly, the class will get 10 marks,
otherwise they will get no mark.
The probability that each of the 5C representatives can answer a question
correctly are 0.6 ,0.8 and 0.75 respectively.

a.) Find the probabilty that the representatives of 5C will give a correct
answer to a question.

b.) Given that 5A and 5B have got 80 and 60 marks respectively,
find the probabolity that 5C will win the contest.
(Give the answer correct to 4 decimal places.)

回答 (1)

Uncle Michael

2008-10-22 8:26 am

✔ 最佳答案

1)
Number of shots attempted by other players
= 150 x [1 - (42% + 20% + 18%)]
= 150 x 20%
= 30 shots

Scoring rate of other players
= (3/30)
= 1/10

=====
2.)
In a pack of 52 cards, there are 26 black cards and 26 red cards.
Among the 26 red cards, 13 are diamond cards.
No. of cards that are not diamond = 52 - 13 = 39

= P(1st card is red diamond, and 2nd card is not diamond)
= (13/52) x (39/51)
= 39/204

= P(1st card is red but not diamond, and 2nd card is not diamond)
= (13/52) x (38/51)
= 38/204

P(1st is red, 2nd is not diamond)
= Sum of the above two probabilities
= (39/204) + (38/204)
= 77/204

=====
3.)a)
rep = representative(s)

P(5C rep give a correct answer to a question)
= P(1st rep correct) + P(2nd rep correct) + P(3rd rep correct)
= (1/3)x0.6 + (1/3)x0.8 + (1/3)x0.75
= 43/60

3.)b)
5C would win the contest will they got 90 marks or 100 marks.
90 marks = 9 correct questions + 1 in correct question
100 marks = 10 correct questions

P(5C wins the contest)
= 10C9x(43/60)9[1-(43/60)] + (43/60)10
= 10 x (43/60)9(17/60) + (43/60)10
= 0.1770
=

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