DSE Probability MCQ

2014-03-12 6:14 pm

有幾條 Probability 想請教一下, 感謝大家
請列式, 最好有埋解釋

1.
A bag contains 2 black balls and 3 white balls. A boy randomly draws balls from the bag one at a time (without replacement) until a white ball appears. Find the probability that he will make at least 2 draws.

2.
A box contains 2 red cards, 3 blue cards and 4 yellow card. Mary repeats drawing one card at a time randomly from the box with replacement until a red card is drawn. Find the probability that Mary needs at least three draws

3.
If a fair die is thrown three times, then the probability that the three numbers thrown are all different is?

回答 (1)

sioieng

2014-03-12 10:49 pm

✔ 最佳答案

1.
W : a white ball is drawn
R : a red ball is drawn

P(at least 2 draws to get W)
= 1 - P(first draw W)
= 1 - (2/5)
= 2/5

OR : P(at least 2 draws to get W)
= P(first drawn R)
= 2/5

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2.
R : a red card is drawn
R' : a blue card or a yellow card is drawn

P(draw R at first two times)
= P(first time R) + P(first time R' and second time R)
= (2/9) + (2/9) x (2/9)
= (2/9) + (4/81)
= 22/81

P(at least three draws to get R)
= 1 - (draw R at first two times)
= 1 - (22/81)
= 59/81

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3.
(1st time: 1 number out of the 6 numbers fulfills the requirement.)
(2nd time: 1 number out of the 5 rest numbers fulfills the requirement.)
(3nd time: 1 number out of the 4 rest numbers fulfills the requirement.)

The requirement probability
= (6/6) x (5/6) x (4/6)
= 5/9

參考: sioieng

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