When randomly choosing 2 cards from a deck of cards without replacement what is the probability of choosing a club and then a heart

Hence, the total probability(P) of randomly choosing 2 cards from a deck of cards without replacement such that the first card is club and then a heart is: 0.06373.

Step-by-step explanation:

We know that in a deck of 52 playing cards the suits are divided into 4:

" Heart, Club,Diamond and Spade"

i.e. there are total 13 cards each which are Heart, Club,Diamond and Spade.

Hence, the probability of choosing the first card to be Club out of total 52 playing cards is:

similarly the probability of choosing second card to be Heart out of 51 playing cards  is:

Hence, the total probability(P) of randomly choosing 2 cards from a deck of cards without replacement such that the first card is club and then a heart is:

Hence,

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form