We are drawing a 5-card hand from a standard 52-card deck a. What is the probability that all the cards are spades? (5pts)

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.

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step-by-step explanation:

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.