? 發問於 科學及數學數學 · 1 十年前

PROBABILITIES》數學不識

PROBABILITIES》數學不識

1. in throwingtwo dice, find the probability of getting

(i)2 even numbers

(ii) 1 even number and 1 odd numbers

2. Bag a contains 4 red balls and 6 green balls. bag b contains 2 red balls and 2 green balls. one ball is randomly drawn from a and put into bag b. then one ball is drawn from bag b randomly. find the probability that the ball drawn from bag bag b is

1)red?

ii)green?

2 個解答

評分
  • 1 十年前
    最愛解答

    1)

    (i)

    P(two even numbers)

    = P(1st dice show even) x P(2nd dice show even)

    = 1/2 x 1/2

    = 1/4

    (ii)

    P(1 even and 1 odd)

    = P(1st dice show even) x P(2nd dice show odd) + P(1st dice show odd) x P(2nd dice show even)

    = 1/2 x 1/2 + 1/2 x 1/2

    = 1/2

    2)

    (i)

    P(red)

    = P(green ball from bag A to B) x P(red ball from bag B) + P(red ball from bag A to B) x P(red ball from bag B)

    = 6/10 x 2/5 + 4/10 x 3/5

    = 24/50

    = 12/25

    解釋

    情況一: 先抽green,再抽green

    由bag A to B時, 10個ball只有6個green, i.e.P(green ball from bag A to B) = 6/10

    當一個green ball被抽到bag B 後, bag B內一共有5個ball,其中有2個red,

    i.e. P(red ball from bag B) = 2/5

    情況二:先抽red,再抽green

    由bag A to B時, 10個ball只有4個red, i.e.P(red ball from bag A to B) = 4/10

    當一個red ball被抽到bag B 後, bag B內一共有5個ball,其中有3個red,

    i.e. P(red ball from bag B) =3/5

    P(抽到red ball) = P(情況一) + P(情況二)

    (ii)

    P(green)

    = P(green ball from bag A to B) x P(green ball from bag B) + P(red ball from bag A to B) x P(green ball from bag B)

    = 6/10 x 3/5 + 4/10 x 2/5

    = 26/50

    = 13/25

    OR

    1 - P(red)

    = 13/25

  • 1 十年前

    1.(i)1/6

    (ii)1/9

    2.(i)1/5

    (ii)3/10

    2010-05-04 19:21:29 補充:

    1(i)9/36=1/4

    (ii)(36-6-(9-3))/36=2/3

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