1
$\begingroup$

Suppose we select 5 cards. What is the probability of getting two or fewer hearts?

N=the number of items in the population m= the number classified as success in the population n= the number of items in the sample x=the number of items in the sample classified as success

When finding the values I came up with:

$N=52$

$n=5$

$x=2$

$m=13$

I found this was incorrect as I solved for $m-n\choose n-x$ I got negative values for $n-x$ and $n-m$

  • 0
    How many ways to get zero hearts? $\binom{13}{0}\cdot \binom{39}{5}$. How many ways to get one heart? $\binom{13}{1}\cdot \binom{39}{4}$. How many ways to get two hearts? $\underline{~~~~~~~~~~}$. Add these together and divide by the number of ways to take five cards regardless of number of hearts. – 2017-02-27

1 Answers 1

2

You should not be getting negative terms in the binomials coefficients using: $N= 52,\\ M=13,\\ n=5,\\ x\in\{0,1,2\}$

$$\begin{align}\mathsf P(X\leq 2) &= \sum\limits_{x=0}^2 \left.\dbinom {M}{x}\dbinom{N-M}{n-x}\middle/ \dbinom{N}{n}\right. \\[1ex] & = \dfrac{\dbinom{13}{0}\dbinom{52-13}{5-0}+\dbinom{13}{1}\dbinom{52-13}{5-1}+\dbinom{13}{2}\dbinom{52-13}{5-2}}{\dbinom{52}5} \end{align}$$

Are you sure you made no transcription oreos?