The question I am currently working with is as follows:
If three cards are randomly selected from a standard 52 card deck of playing cards, what is the probability that at least one of them will be a painted face card (king, queen or jack)?
Initially, I just went ahead and solved it as follows:
P(at least 1 will be a face card) = 1 - (40/52)*(39/51)*(38/50) = 55.29%
However, I went to solve it using the binomial distribution function just out of curiosity and got a slightly different answer:
P(at least 1 will be a face card) = 1 - (3 choose 3) * (40/52)^3 * (12/52)^0 = 54.48%
Why?
Hello, terrorsquid!
If three cards are randomly selected from a standard 52 card deck of cards,
what is the probability that at least one will be a face card (K, Q or J)?
Initially, I just went ahead and solved it as follows:
P(at least 1 face card) = 1 - (40/52)*(39/51)*(38/50) = 55.29%
However, I solved it using the binomial distribution function just out of curiosity
and got a slightly different answer:
P(at least 1 face card) = 1 - (3 choose 3) * (40/52)^3 * (12/52)^0 = 54.48%
Why?
Plato is correct . . . The draws are not independent.
With the binomial function, you are using .for each draw.
. . You are drawing the 3 cards with replacement.
Here's another approach . . .
There are 12 Face cards and 40 Others.
Select 3 cards from the 52 cards.
. . There are: .
Select 3 cards from the 40 Others.
. . There are: .
Thank you! Very helpful.
I am starting a statistics degree next month and was interested in going over probability and some of the topics I will cover in my course. I was wondering if you could recommend any resources (perhaps a textbook) that do a good job of covering some of the major topics that I will come across - just something structured so I can progress through the various components of probability in a logical order.
Thanks.
Here is a great website.
Some where there is a freepdf of a textbook, I think.