In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. the spades and the clubs are black and the hearts and the diamonds are red. if two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

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

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer: can you give the

step-by-step explanation: