Respuesta :
The probability of getting three queens and two 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 three queens and two kings
Now, we know that, in a deck of 52 cards, we will have 4 queens and 4 kings.
[tex]\text { probability of an event }=\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 { Plobability 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 of third queen:
Similarly here favorable outcome = 2, since we already drew 2 queen out of 4
And now number of outcomes = 51 – 1 = 50
[tex]\text { Probability of } 3^{\text {rd }} \text { queen }=\frac{2}{50}=\frac{1}{25}[/tex]
Probability for first king:
Here kings are 4, but overall cards are 49 as 3 queens are drawn
[tex]\text { probability for } 1^{\text {st }} \text { king }=\frac{4}{49}[/tex]
Probability for second king:
Here, kings are 3 and overall cards are 48 as 3 queens and 1 king are drawn
[tex]\text { probability of } 2^{\text {nd }} \text { king }=\frac{3}{48}=\frac{1}{16}[/tex]
And, finally the overall probability to get 3 queens and 2 kings is:
[tex]=\frac{1}{13} \times \frac{1}{17} \times \frac{1}{25} \times \frac{4}{49} \times \frac{1}{16}=\frac{4}{4331600}=\frac{1}{1082900}[/tex]
Hence, the probability is [tex]\frac{1}{1082900}[/tex]
Answer:
Step-by-step explanation:
its .0009234%
I just took the test and this was the answer, I dare you to try it, cuz its right.
