Respuesta :
There are 13 heart cards
Now 1 heart card can be drawn from a pack of 13 heart cards in 13C1 ways
13C1=13
Also,1 card can be drawn from a pack of 52 cards in 52C1 ways
52C1=52
The probability of drawing a heart card from a pack of 52 cards is
13/52=1/4
there are 26 black cards in total
(13 spades +13 clubs)
Now 1 black card can be drawn from a pack of 26 black cards in 26C1 ways
26C1=26
Also,1 card can be drawn from a pack of 52 cards in 52C1 ways
52C1=52
The probability of drawing a black card from a pack of 52 cards is
26/52=1/2
Now as both the task are performed one after the other and after replacement so the probability of drawing a heart after a black card is
=1/2 * 1/4
=1/8
Answer:
[tex]\bf\textbf{The required Probability = }\frac{1}{8}[/tex]
Step-by-step explanation :
Number of heart cards = 13
Number of club cards = 13
Number of diamond cards = 1 3
Number of spades card = 13
[tex]\text{Number of ways of drawing 1 heart card from 13 cards of heart = }_{1}^{13}\textrm{C}=13\\\\\text{Also,no of ways 1 card can be drawn from a pack of 52 cards = }_{1}^{52}\textrm{C}=52\\\\\text{The probability of drawing a heart card from a pack of 52 cards = }\frac{13}{52}=\frac{1}{4}[/tex]
There are 13 spades card and 13 club cards
⇒ Number of black cards = 13 + 13
= 26
[tex]\text{Number of ways of drawing 1 black card from 26 black cards = }_{1}^{26}\textrm{C}=26\\\\\text{Also,no of ways 1 card can be drawn from a pack of 52 cards = }_{1}^{52}\textrm{C}=52\\\\\text{The probability of drawing a black card from a 26 black cards = }\frac{26}{52}=\frac{1}{2}[/tex]
[tex]\textbf{Now, The probability that a black card is chosen first}\\\textbf{and a heart is chosen second = }\frac{1}{4}\times \frac{1}{2}\\\\\bf\implies\textbf{The required Probability = }\frac{1}{8}[/tex]
