Question

If you are dealt 5 cards from a shuffled deck of 52​ cards, find the probability of getting two queens and three kings.

The probability is
nothing.
​(Round to six decimal places as​ needed.)

Answer 1

The probability of getting two queens and three kings is
`(1)/(1082900)`

Solution:

Given that, you are dealt five cards from a shuffled deck of 52 cards

We have to find the probability of getting two queens and three kings

Now, we know that, in a deck of 52 cards, we will have 4 queens and 4 kings.

`{ probability }=\frac{\text { favarable possibilities }}{\text { number of possibilities }}`

Probability of first queen:

`\text { Probability for } 1^{\text {st }} \text { queen }=(4)/(52)=(1)/(13)`

Probability of second queen:

`\text { Probability for } 2^{\text {nd }} \text { queen }=(3)/(51)=(1)/(17)`

Here we used 3 for favourable outcome, since we already drew 1 queen out of 4

And now number of outcomes = 52 – 1 = 51

Probability for first king:

`\text { Probability of } 1^{\text {st }} \text { king }=(4)/(50)=(2)/(25)`

Here favourable outcomes = 4

And now number of outcomes = 51 – 1 = 50

Probability for second king:

`\text { Probability of second king }=(3)/(49)`

Here favourable outcomes = 3, since we already drew 1 king

And now number of outcomes = 50 - 1 = 49

Probability for third king:

`\text { Probability of third king }=(2)/(48)=(1)/(24)`

Here favourable outcomes = 2, since we already drew 2 king

And now number of outcomes = 49 - 1 = 48

Now the total probability of getting 2 queens and 3 kings from a shuffled deck of cards is:

`=(1)/(13) * (1)/(17) * (2)/(25) * (3)/(49) * (1)/(24)=(1)/(1082900)`

Hence, the probability is
`(1)/(1082900)`