Question

Draw a card 8 times from a shuffled deck, with replacement. What is the probability that at least 5 of the draws will be face cards?

Answer 1

\[\left(\begin{matrix}n \\ k\end{matrix}\right)p^k(1-p)^{n-k}\]

Answer 2

n=8
k=5
\[p =\frac{ 3 }{ 13 }\]

Answer 3

somehow i got 0.01668
but the book's answer is 0.01941
did i mistake some numbers or I miss something inside the formula ?

Answer 4

you have to repeat with \(P(x=6),P(x=7)\) and \(P(x=8)\) then add

Answer 5

i would use wolfram

Answer 6

You need to find the probability that exactly 6 will be face cards, then exactly 7 will be face cards and finally that exactly 8 will be face cards. Then add these 3 values of probability to the probability of exactly 5 cards thsat you have already found.

Answer 7

k I will use wolfram would be long calculation

Answer 8

with binomial [8,5](3/13)^5(1-3/13)^3+....

Answer 9

http://www.wolframalpha.com/input/?i=56%283%2F13%29^5%2810%2F13%29^3%2B28%283%2F13%29^6%2810%2F13%29^2%2B8%283%2F13%29^5%2810%2F13%29%2B%283%2F13%29^6

Answer 10

got it

Answer 11

btw don't write \(1-\frac{3}{13}\) since that is clearly \(\frac{10}{13}\)

Answer 12

http://www.wolframalpha.com/input/?i=binomial+%5B8%2C5%5D%283%2F13%29%5E5%281-3%2F13%29%5E3%2Bbinomial+%5B8%2C6%5D%283%2F13%29%5E6%281-3%2F13%29%5E2%2Bbinomial+%5B8%2C7%5D%283%2F13%29%5E7%281-3%2F13%29%5E1%2Bbinomial+%5B8%2C8%5D%283%2F13%29%5E8%281-3%2F13%29%5E0

Answer 13

i guess my calculation in wolfram is correct while this is a bit odd
http://www.wolframalpha.com/input/?i=56%283%2F13%29^5%2810%2F13%29^3%2B28%283%2F13%29^6%2810%2F13%29^2%2B8%283%2F13%29^5%2810%2F13%29%2B%283%2F13%29^6

Answer 14

both are bit similar http://www.wolframalpha.com/input/?i=56%283%2F13%29%5E5%2810%2F13%29%5E3%2B28%283%2F13%29%5E6%2810%2F13%29%5E2%2B7%283%2F13%29%5E7%2810%2F13%29%5E1%2B1%283%2F13%29%5E8%2810%2F13%29
and
http://www.wolframalpha.com/input/?i=binomial+%5B8%2C5%5D%283%2F13%29%5E5%281-3%2F13%29%5E3%2Bbinomial+%5B8%2C6%5D%283%2F13%29%5E6%281-3%2F13%29%5E2%2Bbinomial+%5B8%2C7%5D%283%2F13%29%5E7%281-3%2F13%29%5E1%2Bbinomial+%5B8%2C8%5D%283%2F13%29%5E8%281-3%2F13%29%5E0

Answer 15

thank you both for help @satellite73 and @kropot72

Answer 16

closing this now because the question is already answer

Answer 17

You're welcome :)