Mathematics, 31.07.2019 20:20, tadopson2003

Ga standard deck of playing cards is shuffled and three people each choose a card. find the probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement, and if the cards are chosen without replacement. (a) the cards are chosen with replacement. (b) the cards are chosen without replacement.

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The probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement is 0.03125 .

The probability that the first two cards chosen are spades and the third card is red if the cards are chosen without replacement is 0.03058

Step-by-step explanation:

Total no. of cards = 52

Spade cards = 13 (Black)

Club cards = 13 (Black)

Heart cards = 13 (Red)

Diamond cards = 13(Red)

Total red cards = 26

With replacement case:

Probability of getting spade on first draw = $\frac{13}{52}$

Now card is replaced

Probability of getting spade on second draw = $\frac{13}{52}$

Now card is replaced

Probability of getting red card on third draw = $\frac{26}{52}$

So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement = $\frac{13}{52} \times \frac{13}{52} \times \frac{26}{52}$

= $\frac{1}{32}$

= 0.03125

Without replacement case:

Probability of getting spade on first draw = $\frac{13}{52}$

Remaining cards = 51

Remaining spade cards = 12

Probability of getting spade on second draw = $\frac{12}{51}$

Remaining cards = 50

Probability of getting red card on third draw = $\frac{26}{50}$

So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen without replacement = $\frac{13}{52} \times \frac{12}{51} \times \frac{26}{50}$

= $\frac{13}{425}$

= 0.03058

Hence The probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement is 0.03125 . The probability that the first two cards chosen are spades and the third card is red if the cards are chosen without replacement is 0.03058

answered: Guest

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answered: Guest

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Ga standard deck of playing cards is shuffled and three people each choose a card. find the probabil...