PROBABILITIES》數學不識

Question

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?

Answer 1

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

Answer 2

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