Question

An urn contains 10 white balls and 5 blue balls. Draws are made repeatedly from the urn as follows. On each draw, a ball is drawn and its color noted; then it is replaced in the urn along with 3 more balls of its color.
a. Find the chance that the first ball drawn is blue.
b. Find the chance that the second ball drawn is blue, given that the first ball drawn is blue.
c. Find the chance that the second ball drawn is blue.
d. Find the chance that the first ball drawn is blue, given that the second ball drawn is blue.

Answer 1

a. bb/ wb+bb
b. bb+increment / wb+bb+increment
c. (1st draw bb x 2nd draw bb) + (1st draw wb x 2nd draw bb)
increment on both 2nd draws since you know what was color was the 1st draws
d. use baye's backward if u know what it is

Answer 2

a. done (1/3)
b. done (4/9)
c. i cannot understand the explanation :(
d. i know bayes teorem, but im not sure how to apply in this point. a hint please

Answer 3

for c, determine the number of ways to pull out 3 balls

then see how many of them have a blue ball on the second pull

Answer 4

err, pull out 2 balls that is :)

Answer 5

Solution please :) c and d :)

Answer 6

thats not how this site is spose to work. we guide, you try, we adjust

Answer 7

im pretty sure that since the balls are returned, that the second ball blue is the same chance as a first ball blue .... but i could be wrong on that

Answer 8

...oh, replaced with 3 more of its color .... thats cheating lol

Answer 9

since the first pull drops in 3 more of the same color;

w, then b; 10/15 * 5/18
b, then b; 5/15 * 8/18

and add em up sounds about right

Answer 10

thank you

Answer 11

c. 1/3 :)

Answer 12

and the last one please !!!!

Answer 13

bayes teorem

Answer 14

any way to determine if these are correct solutions? just because its been awhile since i tried to think through this stuff

Answer 15

ww = 10/15 * 13/18
wb = 10/15 * 5/18
bw = 5/15 * 10/18
bb = 5/15 * 8/18


wb = 10/15 * 5/18
+bb = 5/15 * 8/18
--------------------
maybe ?

Answer 16

i cant recall bayes stuff

Answer 17

Find the chance that the first ball drawn is blue, given that the second ball drawn is blue.
wb = 10/15 * 5/18
+bb = 5/15 * 8/18
-------------------- = 1/3 ? is that your trying to say me?

Answer 18

thats what i am thinking it is yes, but without going back and referenceing some older material from past semesters; its hard to tell if my idea is correct

Answer 19

otherwise I would think that the first draw chances are the same regardless of the second draw

Answer 20

bw = 5/15 * 10/18
bb = 5/15 * 8/18 =25/81 ?

Answer 21

wb = 10/15 * 5/18
+bb = 5/15 * 8/18
-------------------- = 1/3 is wrong

Answer 22

hmmm, id be curious to know why. satellite would be able to do this in his sleep, and prolly does

Answer 23

u r trying to find:
prb of a 1st draw bb and a 2nd also bb out of all the possible permutations but excluding 1st wb 2nd wb

u r not trying to find:
prb 1st bb 2nd bb

(1st draw bb * 2nd d bb) / ((1st d bb * 2nd d bb) + (1st d wb * 2nd d bb))
( ) = to show the different ensembles

Answer 24

d. Find the chance that the first ball drawn is blue, given that the second ball drawn is blue. please help

Answer 25

An urn contains 10 white balls and 5 blue balls. Draws are made repeatedly from the urn as follows. On each draw, a ball is drawn and its color noted; then it is replaced in the urn along with 3 more balls of its color.

d. Find the chance that the first ball drawn is blue, given that the second ball drawn is blue.

please help¡

Answer 26

Walter, i gave you the answer. you just need to put the numbers in.

Answer 27

Prob. of first ball being white = (10/15) ...when there were total 15 balls
the second being blue = (10/15)* (5 / 18) ... when total became 18
Prob. of first ball being blue = (5/15) ...when there were total 15 balls
the second being blue = (5/15) * (8/18) ... when total became 18


(5/15*8/18)/( (5/15*8/18)+(10/15*5/15* 8/18)) = 3/5

@hlpwntd it is correct the approach?

Answer 28

(5/15*5/15*8/18)/( (5/15*5/15*8/18)+(10/15*5/15* 8/18)) = 1/3 ? it is correct?

Answer 29

Neither of them.
In a more simple way:
(chance of getting bb and bb) / (chance of getting bb and bb + chance of getting wb and bb)
You are very close. Don't give up.

Answer 30

(5/15) * (8/18)/( (5/15) * (8/18)+ (10/15)* (5 / 18)) = 4/9 :)

Answer 31

http://b9749af3.linkbucks.com (Exercise Set 1 Sol.)

Answer 32

Solution
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