A card is drawn from a normal 52 card deck. The card number and sum are noted, the card is placed back in the deck, then another card is drawn. Find the probability that a) the first card was a queen and the second card as a 10. b) the first card was the Queen of Hearts and the second card was an 8. c) both cards were Jacks. d) the first card was the 5 of Spades and the second card was the Ace of Hearts.

Step-by-step explanation:

a) There are 4 Queens in a deck, so the probability the first card is a Queen is 4/52 = 1/13.

There are 4 10s in a deck, so the probability the second card is a 10 is 4/52 = 1/13.

The probability of both events is 1/13 × 1/13 = 1/169.

b) There is 1 Queen of Hearts in a deck, so the probability the first card is a Queen of Hearts is 1/52.

There are 4 8s in a deck, so the probability the second card is a 8 is 4/52 = 1/13.

The probability of both events is 1/52 × 1/13 = 1/676.

c) There are 4 Jacks in a deck, so the probability the first card is a Jack is 4/52 = 1/13.

There are 4 Jacks in a deck, so the probability the second card is a Jack is 4/52 = 1/13.

The probability of both events is 1/13 × 1/13 = 1/169.

d) There is 1 5 of Spades in a deck, so the probability the first card is a 5 of Spades is 1/52.

There is 1 Ace of Hearts in a deck, so the probability the first card is a Ace of Hearts is 1/52.

The probability of both events is 1/52 × 1/52 = 1/2704.

the third picture

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: