Question

9. What is the probability of drawing three cards, without replacement
,

from a deck of cards and getting three kings?​

Answer 1

Answer:

The probability of getting three kings without replacement is $\frac{1}{5525}$ ≈ 0.018%

Step-by-step explanation:

Solution:

Total number of cards = 52

Total number of kings= 4

We have find the probability of getting three kings

Step 1:

For the first draw, there are 52 cards.

In the first draw we have four kings in the deck.

The probability of first draw = $\frac{4}{52}$

                                              = $\frac{1}{13}$

Step 2:

For the second draw , there are 51 cards with three king left.

In the second draw we have three kings in the deck.

The probability of second draw = $\frac{3}{51}$

                                                     = $\frac{1}{17}$

Step 3:

For the third draw, thee are 50 cards with two kings left.

In the third draw we have two kings in the deck.

The probability of third draw = $\frac{2}{50}$

                                               = $\frac{1}{25}$

Therefore the probability is the product of all outcomes of these probability

⇒ $\frac{1}{13} .\frac{1}{17} .\frac{1}{25}$

⇒ $\frac{1}{5525}$

$\frac{1}{5525}$ = 0.018%

Final answer:

The probability of getting three kings without replacement is $\frac{1}{5525}$ ≈ 0.018%

#SPJ3

Answer 2

Answer:

Concept:

Probability means event to occur. It is a branch of mathematics that deals with the random of a random event. The value is expressed from zero to one. Probability was introduced in mathematics to predict how likely events are to occur.

Find:

We find the probability

Given:

three cards, without replacement from a deck of cards and getting three kings

Explain:

Total number of cards = 52

Total number of kings= 4

We have find the probability of getting three kings

Step 1:

For the first draw, there are 52 cards. In the first draw we have four kings in the deck.

The probability of first draw = 4/52 = 1/13

Step 2:

For the second draw, there are 51 cards with three king left.

In the second draw we have three kings in the deck.

The probability of second draw = 3/51 = 1/17

Step 3:

For the third draw, thee are 50 cards with two kings left.

In the third draw we have two kings in the deck. The probability of third draw = 2/50 = 1/25

Therefore the probability is the product of all outcomes of these probability

$\frac{1}{15} \times \frac{1}{17} \times \frac{1}{25}$

$\frac{1}{5525}$

=0.018%

The probability of getting three kings without replacement is 0.018%