Question

You are a member of a class of 18 students. A bowl contains 18chips: 1 blue and 17 red. Each student is to take 1 chip from the bowl without replacement. The student who draws the blue chip is guaranteed an A for the course.
a) If you have a choice of drawing first, fifth or last, which position would you choose? Justify your choice on the basis of probability.
b) Suppose the bowl contains 2blue and 16 red chips. What position would you now choose?
Please, help

Answer 1

@mathstudent55

Answer 2

For A, I'd say fifth.
First means that odds are 17:1
Fifth means odds are 1:12
Last means odds are 1:17

Answer 3

I don't get. I am sorry, Please, give me more explanation

Answer 4

If you go first, then there are eighteen chips, and only one of those eighteen chips is the one you want, so you'd have a \(\frac{1}{18}\)) or 5% chance of getting blue.

Answer 5

If you go fifth, since I'm assuming they don't put the chips back after each drawing and no one else has gotten a blue one, The possibility of you getting the blue chip goes up about .5% every time a person draws one, so you have a 7% chance of getting blue.

Answer 6

If you go last, you have the same probability of getting red as the first person would (5%) because you're hoping that one out of a total of eighteen chips has the blue one.

Answer 7

What if one of the first four get the blue, then the possibility to get blue at the 5th is 0, right?

Answer 8

Yes, but if the first four got blue, the probability of getting it as the last one is zero as well. That's why they're called odds- you just take your chances at whatever position stacks the least odds against you. In this case, the fifth position has greater odds than the first or last.

Answer 9

And for b, I'd say the same thing. First and last have about the same chance (First has better chances than last, but fifth has fewer choices, which gives them a better chance of finding one of the two blues)

Answer 10

Thanks for the help. I need time to digest it. :)

Answer 11

@rational guide me please. I don't get what he said

Answer 12

Is this from binomial distributions ?

Answer 13

yes

Answer 14

Since choosing chips is an random event, it should not matter what position you choose

Answer 15

lets calculate probabilities for first, fifth and last positions to be fully sure

Answer 16

Yes, that 's what I want.

Answer 17

But I don't know how to make it in logic.

Answer 18

ive clicked on another question by mistake and lost all the work ive written so far :/

Answer 19

a) If you have a choice of drawing first, fifth or last, which position would you choose? Justify your choice on the basis of probability.

Answer 20

:) Thanks for being here. I have time.

Answer 21

probability of getting "blue chip" in the `first draw` is 1/18
yes ?

Answer 22

yup

Answer 23

lets find probabilty of getting "blue chip" in the `fifth draw`,

lets define below events :
A : getting "blue chip" in fifth draw
B : getting "red chips" in previous four draws

\(\large P(A\cap B) = P(A|B)*P(B)\)

find the probabilities and plugin

Answer 24

\(P(A|B) = \dfrac{1}{14}\)
yes ?

Answer 25

don't get.

Answer 26

which part

Answer 27

1/14

Answer 28

whats the meaning of P(A|B) ?

Answer 29

the probability of event A given event B occurs

Answer 30

probability of "getting blue chip in fifth draw" given that "all previous draws are red"
yes ?

Answer 31

oh, ye,

Answer 32

got it,

Answer 33

So at fifth draw,
you have 14 chips in total in the bowl
and only 1 of them is blue

so the probability of getting blue chip wud be 1/14

Answer 34

find P(B) also and plugin

Answer 35

its simple combinatorics :

P(B) = (number of ways for choosing four red chips)/(total number of ways of choosing chips)

Answer 36

\[\dfrac{17}{18}\dfrac{16}{17}\dfrac{15}{16}\dfrac{14}{15}=\dfrac{14}{18}\]

Answer 37

since there are 17 red chips :
P(B) = (17C4)/(18C4)

Answer 38

oh, yeeeeeeeeeees, It makes perfect sense.!! You save my life..:)

Answer 39

Thank you sooooo much.

Answer 40

this has a nice derivation
http://www.math.miami.edu/~igrigore/teaching/mth224/notes_cond_prob.pdf

Answer 41

Thanks for the link.