Respuesta :
The probability of getting two queens and three kings is [tex]\frac{1}{1082900}[/tex]
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.
[tex]{ probability }=\frac{\text { favarable possibilities }}{\text { number of possibilities }}[/tex]
Probability of first queen:
[tex]\text { Probability for } 1^{\text {st }} \text { queen }=\frac{4}{52}=\frac{1}{13}[/tex]
Probability of second queen:
[tex]\text { Probability for } 2^{\text {nd }} \text { queen }=\frac{3}{51}=\frac{1}{17}[/tex]
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:
[tex]\text { Probability of } 1^{\text {st }} \text { king }=\frac{4}{50}=\frac{2}{25}[/tex]
Here favourable outcomes = 4
And now number of outcomes = 51 – 1 = 50
Probability for second king:
[tex]\text { Probability of second king }=\frac{3}{49}[/tex]
Here favourable outcomes = 3, since we already drew 1 king
And now number of outcomes = 50 - 1 = 49
Probability for third king:
[tex]\text { Probability of third king }=\frac{2}{48}=\frac{1}{24}[/tex]
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:
[tex]=\frac{1}{13} \times \frac{1}{17} \times \frac{2}{25} \times \frac{3}{49} \times \frac{1}{24}=\frac{1}{1082900}[/tex]
Hence, the probability is [tex]\frac{1}{1082900}[/tex]
