Probability Problems

2008-05-24 2:34 am

1. A number is chosen at random from natural numbers 1 to 90. What are the probabilities of the following events?
(i) The number chosen is divisible by 3.
(ii) The number chosen is a multiple of 4.
(iii) The number has two digits which add up to 5.

THZ! =]

回答 (1)

None

2008-05-24 5:13 am

✔ 最佳答案

這類型的概率問題無特別的速算方法要自己列出所有可能性

a,b還好可以除出來算 c要想什麼數符合條件十位加個位=5 真的要數

a) 因為 1至90 中有 30 個 3的倍數 (3,6,9,...,87, 90) 所以

P(number choosen is divisible by 3) = 30/90 = 1/3

b) 因為 1至90 中有 22個4的倍數 (4,8,16,...,84,88)

P(number choosen is divisible by 4) = 22/90 = 11/45

c)

因為兩位相加 = 5 只有以下可能 (0,5) (1,4) (2,3) 所以只要考慮1至50中的可能性即是 05, 14, 23, 32, 41 , 50 = 6個

P (number choosen has two digits which add up to 5) = 6/90 = 1/15

參考: 個人理解

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