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lisabon 2012 [21]
3 years ago
6

Three cards are drawn from a standard deck of 52 cards without replacement. Find the probability that the first card is an ace,

the second card is a three, and the third card is a jack.
Mathematics
1 answer:
MrRissso [65]3 years ago
4 0

Answer:

4.82\cdot 10^{-4}

Step-by-step explanation:

In a deck of cart, we have:

a = 4 (aces)

t = 4 (three)

j = 4 (jacks)

And the total number of cards in the deck is

n = 52

So, the probability of drawing an ace as first cart is:

p(a)=\frac{a}{n}=\frac{4}{52}=\frac{1}{13}=0.0769

At the second drawing, the ace is not replaced within the deck. So the number of cards left in the deck is

n-1=51

Therefore, the probability of drawing a three at the 2nd draw is

p(t)=\frac{t}{n-1}=\frac{4}{51}=0.0784

Then, at the third draw, the previous 2 cards are not replaced, so there are now

n-2=50

cards in the deck. So, the probability of drawing a jack is

p(j)=\frac{j}{n-2}=\frac{4}{50}=0.08

Therefore, the total probability of drawing an ace, a three and then a jack is:

p(atj)=p(a)\cdot p(j) \cdot p(t)=0.0769\cdot 0.0784 \cdot 0.08 =4.82\cdot 10^{-4}

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