Question

I am confused about expected number of cards ..

Six cards are removed from a pack (ie. 2 queens and 4 kings). The cards are shuffled and one card at a time is removed until a queen is chosen. X is the probability distribution the number of cards chosen until the first queen appears .
x 0 1 2 3 4
P(X=x) 2/6 8/30 24/120 2/15 24/360
Calculate the expected number of cards that would be need to be chosen before a queen is selected.

Answer 1

is it wrong to say
E(X)= 0*(2/6) + 1*(8/30) +2*(24/120)..... and get 4/3

Answer 2

i dont know why the answer shows ...
E(X)=0*(4/3) + 1*(8/30) + 2*(24/130)..... and ans shows 4/3

i got the same answer as the book states, however my expected value for 0 is different to the book.

Answer 3

fyi that prob distribution table was given in the question

x 0 1 2 3 4
P(X=x) 2/6 8/30 24/120 2/15 24/360

Answer 4

your method is correct! :)
there could be a typing error in the question or in the answer in your book.
luckily, the answer didn't change because the erroneous number is multiplied to 0 :P

Answer 5

yes true. but while i have you here, could you please explain a bit more ..
so table shows number of cards that need to be chosen before a queen appears ..

if 0 cards are chosen - does that mean
Q Q Q Q Q' Q'

Answer 6

can u explain how they got 2/6 for 0 in the table please

Answer 7

sure,

x : number of cards chosen until the first queen appears
x= 0 means the very first card chosen is a Queen!

so what is the probability to choose a Queen from 2 Queens and 4 Kings??

total = 2+4 = 6
probability = 2/6

got it ?

Answer 8

do you also want an explanation how we get 8/30 for x =1 ?

Answer 9

yes plz

Answer 10

x : number of cards chosen until the first queen appears
x= 1 means the second card chosen is a Queen!
which means that the first card chosen MUST be the king.

so what is the probability to choose a King first "AND" then a Queen from (2 Queens and 4 Kings)??
[remember we multiply probabilities for AND and add for OR]

probability of choosing a King from (2 Queens and 4 Kings) = 4/6

now there are only 5 cards remaining, king is already chosen,
(2 Queens and 3 Kings)

now we choose a Queen from these,
probability = 2/5 (2 Queens from total 5 cards)

so total probability = (4/6)* (2/5) = 8/30

Answer 11

oh right, i have started to draw a tree. and starting to get all the other values too and that is also helping me. I really appreciate your time. thank you so much.

Answer 12

i sort of misread the question and thought any 6 cards out of 52 cards, that why i was writing funny stuff at the top lol

Answer 13

ohh! :P it happens :)
welcome ^_^