一個半徑5cm的圓形鏢靶,在鏢靶內晝出兩個半徑分別為1cm和2cm的小圓a和b,若把飛鏢隨意擲出並擲中鏢靶,求下列的概率
(1) 擲中圓a
(2)擲中圓b
(3)既擲不中圓a,又擲不中圓b
要步驟
急急急急急急急
F3 概率 關於圓 急急急急急急!!!
2011-12-04 2:53 am
回答 (3)
2011-12-04 5:28 am
✔ 最佳答案
要先知道圓的面積是: 半徑×半徑×圓周率P(擲中圓a)
(1)(1)(3.1415)÷(5)(5)(3.1415)
=1÷25
P(擲中圓B)
(2)(2)(3.1415)÷(5)(5)(3.1415)
=4÷25
P(既擲不中圓a,又擲不中圓b)
(1-(1÷25)(4÷25))÷(5)(5)(3.1415)
=0.012651281
唔知你取幾位小數
2011-12-04 4:36 pm
1)圓a面積 = ( Π x 1^2)cm^2 = Π cm^2
鏢靶面積 = ( Π x 5^2)cm^2 = 25Π cm^2 P(擲中圓a) = Π cm^2 / 25Π cm^2 = 1/25 2)圓b面積 = ( Π x 2^2 - Π x 1^2 )cm^2 = 3 Π cm^2
P(擲中圓b) = 3 Π cm^2 / 25Π cm^2 = 3/253)P(不中圓a和圓b)= 1 - 1/25 - 3/25 = 21/25 不用解釋,擲中鏢靶,不中圓a和圓b
鏢靶面積 = ( Π x 5^2)cm^2 = 25Π cm^2 P(擲中圓a) = Π cm^2 / 25Π cm^2 = 1/25 2)圓b面積 = ( Π x 2^2 - Π x 1^2 )cm^2 = 3 Π cm^2
P(擲中圓b) = 3 Π cm^2 / 25Π cm^2 = 3/253)P(不中圓a和圓b)= 1 - 1/25 - 3/25 = 21/25 不用解釋,擲中鏢靶,不中圓a和圓b
2011-12-04 3:29 am
find the corresponding area first
circle 'a' = pi (a^2)
cricle 'b' = a^2 = pi (b^2 - a^2)
rest = pi (5^2 - b^2)
P(circle 'a') = pi (a^2) / pi (5^2) = a^2/25
P(circle 'b') = pi (b^2 - a^2) / pi (5^2) = (b^2 - a^2) / 25
P(rest) = pi (25-b^2) / pi (5^2) = (25-b^2) / 25
circle 'a' = pi (a^2)
cricle 'b' = a^2 = pi (b^2 - a^2)
rest = pi (5^2 - b^2)
P(circle 'a') = pi (a^2) / pi (5^2) = a^2/25
P(circle 'b') = pi (b^2 - a^2) / pi (5^2) = (b^2 - a^2) / 25
P(rest) = pi (25-b^2) / pi (5^2) = (25-b^2) / 25
收錄日期: 2021-04-13 18:23:19
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