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You are dealt two cards successively without replacement from a standard deck of 52 playing cards. find the probability that the first card is a two and the second card is a ten. round your answer to three decimal places

Respuesta :

we have four two cards in 52 cards and four ten cards in the same playing cards 
to get our first four cards we choose one from the whole set of 52 cards
but to get the next card with ten we choose them out of 51 because we took the first card with value two and we have not replaced it
this gives us
4/52*4/51=0.006
MrRoyal

The probability that the first card is 2, and the second card is 10 is 0.006

In a standard deck of cards, we have:

[tex]n(2) = 4[/tex] -- number of cards numbered 2

[tex]n(10) = 4[/tex] -- number of cards numbered 4

[tex]n = 52[/tex] --- the total number of cards in a standard deck

The selection of each card is without replacement.

So, the probability that the first is 2, and the second is 10 is:

[tex]Pr = \frac{n(2)}{n} \times \frac{n(10)}{n-1}[/tex]

So, we have:

[tex]Pr = \frac{4}{52} \times \frac{4}{52-1}[/tex]

Subtract 1 from 52

[tex]Pr = \frac{4}{52} \times \frac{4}{51}[/tex]

Multiply

[tex]Pr = \frac{16}{2652}[/tex]

Divide

[tex]Pr = 0.006[/tex]

Hence, the probability is 0.006

Read more about probabilities at:

https://brainly.com/question/11234923

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