有關Probabilities
謝謝
1.
In throwing two dice ,find the probability of getting
(a) 2 even numbers
(b) 1 even number and 1 odd numbers
2.
In a school, there are 380 boys and 420 girls, and 45% of boys and 40% of girls are wearing glasses. If a student chosen randomly from the school is
wearing glasses. Find the probability that it is a boy.
3.
The probability that door is locked is 2/3. In a bunch of 5 keys, 1 key can
unlock the door. What is the probability that a man can open the door by
choosing 2 keys randomly ?
詳細解答 ..
謝謝..
F4 Maths (有關Probabilities)
2012-05-03 11:28 pm
回答 (2)
2012-05-03 11:57 pm
✔ 最佳答案
1(a) P(getting 1 even numbers)=1/2
P(getting 2 even numbers)
=1/2* 1/2
=1/4 //
1(b) P(getting 1 odd numbers)
=1/2
P(getting 1 odd no., then 1 even no.) + P(getting 1 even no. , then 1 odd no.)
=1/2 * 1/2 + 1/2 * 1/2
=1/4 + 1/4 =2/4
=1/2 //
2. P(students wearing glasses) =380*0.45 + 420*0.4 =171+168
=339
P(boy who wearing glasses| students wearing glasses)
=171/339
=57/113 //
3.P(the door is unlocked) =1/3
P(can open the door )= 1/3 + 2/3 * 2/5 =1/3 + 4/15 =5/15 + 4/15 =9/15
=3/5 //
2012-05-03 11:51 pm
1a) 1/2 x 1/2 = 1/4 (even die had half chance of even)
1b) 1/2 x 1/2 + 1/2 x 1/2 = 1/4 + 1/4 = 1/2 (same as above, but can be odd+even and even+odd, they are different-imagine two die of different color!)
2(conditional probabiltiy)
= 380x0.45 (those are boys)
380x0.45+420x0.4 (all students with glasses)
= 0.5044
3.P(can open) = 1 - P(can't open)
P(can't open) = 2/3 x 4/5 x 3/4 (2/3 chance of lock, then 4/5 first key wrong, then 4 keys remain with 3 key wrong, therefore 3/4)
pm me if anything still unclear.
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1b) 1/2 x 1/2 + 1/2 x 1/2 = 1/4 + 1/4 = 1/2 (same as above, but can be odd+even and even+odd, they are different-imagine two die of different color!)
2(conditional probabiltiy)
= 380x0.45 (those are boys)
380x0.45+420x0.4 (all students with glasses)
= 0.5044
3.P(can open) = 1 - P(can't open)
P(can't open) = 2/3 x 4/5 x 3/4 (2/3 chance of lock, then 4/5 first key wrong, then 4 keys remain with 3 key wrong, therefore 3/4)
pm me if anything still unclear.
若覺得我幫到你，請到我的 Facebook Page 比個 Like 我，感激！
經數學人
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參考: 經數學園 http://ronaldchik.blogspot.com
收錄日期: 2021-04-23 22:11:28
原文連結 [永久失效]:
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