Question

Cenntura was having fun playing poker she needed the next two cards out to be heart so she could make a flesh five cards of the same suit there are 10 cards left on the deck and three our hearts what is the probability that two cards doubt to Seterra without replacement will both be hearts answer choices are in percentage for format rounded to the nearest whole number

Answer 1

7% probability that the next 2 cards are hearts.

Explanation:

Cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

10 cards, which means that
`N = 10`

3 are hearts, which means that
`k = 3`

Probability that the next 2 cards are hearts:

This is P(X = 2) when n = 2. So

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

`P(X = 2) = h(2,10,2,3) = (C_(3,2)*C_(7,0))/(C_(10,2)) = 0.0667`

0.0667*100% = 6.67%

Rounded to the nearest whole number, 7% probability that the next 2 cards are hearts.