Answer:
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 =
Now card is replaced
Probability of getting spade on second draw =
Now card is replaced
Probability of getting red card on third draw =
So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement =
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Without replacement case:
Probability of getting spade on first draw =
Remaining cards = 51
Remaining spade cards = 12
Probability of getting spade on second draw =
Remaining cards = 50
Probability of getting red card on third draw =
So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen without replacement =
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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