Ifyou are deall 3 cards from a shumied deck of 52 cards, find the probability that all 3 cards are
diamonds.
The probability is .
(Round to six decimal places as needed.)

Question

Ifyou are deall 3 cards from a shumied deck of 52 cards, find the probability that all 3 cards are diamonds. The probability is $$ \square $$. (Round to six decimal places as needed.)

UpStudy AI · Accepted Answer

To find the probability that all 3 cards drawn from a shuffled deck of 52 cards are diamonds, we need to calculate the probability of drawing 3 diamonds in a row.

The probability of drawing a diamond on the first draw is $$ \frac{13}{52} $$ since there are 13 diamonds in a deck of 52 cards.

The probability of drawing a diamond on the second draw, given that the first card drawn was a diamond, is $$ \frac{12}{51} $$ since there are now 12 diamonds left in a deck of 51 cards.

The probability of drawing a diamond on the third draw, given that the first two cards drawn were diamonds, is $$ \frac{11}{50} $$ since there are now 11 diamonds left in a deck of 50 cards.

Therefore, the probability that all 3 cards drawn are diamonds is the product of these probabilities:

$$ P(\text{all 3 cards are diamonds}) = \frac{13}{52} \times \frac{12}{51} \times \frac{11}{50} $$

Let's calculate this probability.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\frac{\frac{13}{52}\times 12}{51}\times 11}{50}$$
- step1: Reduce the fraction:
  $$\frac{\frac{\frac{1}{4}\times 12}{51}\times 11}{50}$$
- step2: Reduce the fraction:
  $$\frac{\frac{1}{17}\times 11}{50}$$
- step3: Multiply:
  $$\frac{\frac{11}{17}}{50}$$
- step4: Multiply by the reciprocal:
  $$\frac{11}{17}\times \frac{1}{50}$$
- step5: Multiply the fractions:
  $$\frac{11}{17\times 50}$$
- step6: Multiply:
  $$\frac{11}{850}$$
The probability that all 3 cards drawn from a shuffled deck of 52 cards are diamonds is approximately 0.012941 or $$ \frac{11}{850} $$.
The probability that all 3 cards drawn are diamonds is approximately 0.012941.

Ifyou are deall 3 cards from a shumied deck of 52 cards, find the probability that all 3 cards are
diamonds.
The probability is .
(Round to six decimal places as needed.)

Upstudy AI Solution

Answer

Solution

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Ifyou are deall 3 cards from a shumied deck of 52 cards, find the probability that all 3 cards are diamonds. The probability is . (Round to six decimal places as needed.)

Upstudy AI Solution

Answer

Solution

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Latest Probability Questions

Ifyou are deall 3 cards from a shumied deck of 52 cards, find the probability that all 3 cards are
diamonds.
The probability is .
(Round to six decimal places as needed.)