Answer:
The probability that the first card is a Heart and the second card is a Spade is 0.064.
Step-by-step explanation:
A standard deck of 52 cards is shuffled and two cards are drawn without replacement.
The denominations of the cards are as follows:
Spades (S) = 13
Hearts (H) = 13
Diamonds (D) = 13
Clubs (C) = 13
Compute the probability of selecting a Heart first as follows:
[tex]P(H)=\frac{13}{52}=0.25[/tex]
Compute the probability of selecting a Spade second as follows:
[tex]P(S)=\frac{13}{51}=0.255[/tex]
Since the two cards are selected without replacement the second draw is independent of the other.
Then the probability that the first card is a Heart and the second card is a Spade is:
[tex]P(1st\ H\cap 2nd\ S)=P(H)\times P(S)[/tex]
[tex]=0.25\times 0.255\\=0.06375\\\approx 0.064[/tex]
Thus, the probability that the first card is a Heart and the second card is a Spade is 0.064.
