Answer:
0.0005 = 0.05% probability that all the cards are spades.
Step-by-step explanation:
The cards are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
52 cards means that N = 52.
13 of the cards are spades, which means that k = 13.
5 card hand means that n = 5.
What is the probability that all the cards are spades?
This is P(X = 5). So
0.0005 = 0.05% probability that all the cards are spades.