Respuesta :
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 = [tex]\frac{13}{52}[/tex]
Now card is replaced
Probability of getting spade on second draw = [tex]\frac{13}{52}[/tex]
Now card is replaced
Probability of getting red card on third draw = [tex]\frac{26}{52}[/tex]
So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen with replacement = [tex]\frac{13}{52} \times \frac{13}{52} \times \frac{26}{52}[/tex]
=[tex]\frac{1}{32}[/tex]
= [tex]0.03125[/tex]
Without replacement case:
Probability of getting spade on first draw = [tex]\frac{13}{52}[/tex]
Remaining cards = 51
Remaining spade cards = 12
Probability of getting spade on second draw = [tex]\frac{12}{51}[/tex]
Remaining cards = 50
Probability of getting red card on third draw = [tex]\frac{26}{50}[/tex]
So, The probability that the first two cards chosen are spades and the third card is red if the cards are chosen without replacement = [tex]\frac{13}{52} \times \frac{12}{51} \times \frac{26}{50}[/tex]
= [tex]\frac{13}{425}[/tex]
= [tex]0.03058[/tex]
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
