Two cards are drawn from a standard deck of cards.
Part A: If they are drawn with replacement, what is the probability that both cards are 7s?
Part B: If they are drawn without replacement, what is the probability that the first card is a club and the second card is a heart?
Part C: Which of the two scenarios in Part A or Part B represents dependent events? Explain.
+2592 Part A: 4 7's ina deck of 52 right?
So it's 4/52 if a 7 gets drawn?
4/52 = 2/26 = 1/13
So it's a 1 in 13 chance of a 7 getting drawn
Do that twice
1/169 chance
Part B: First draw, it's a one in 4 chance of getting a heart, due to 13 cards of each suite in a 52 card deck.
But then it is a 13 in 51 chance for the heart, due to the non-replacement
13/51 * 1/4 = 13/204 chance of getting that combination
Part C: B is a dependent even due to the cards being drawn depending on the cards previously drawn. If you draw a Spade, then instead of a 13/52 chance, you have a 12/51 chance of drawing another spade. And etc. till you get to a 1/40 chance of getting a spade, if you, somehow, get 11 consecutive spades.
+2592 Part A: 4 7's ina deck of 52 right?
So it's 4/52 if a 7 gets drawn?
4/52 = 2/26 = 1/13
So it's a 1 in 13 chance of a 7 getting drawn
Do that twice
1/169 chance
Part B: First draw, it's a one in 4 chance of getting a heart, due to 13 cards of each suite in a 52 card deck.
But then it is a 13 in 51 chance for the heart, due to the non-replacement
13/51 * 1/4 = 13/204 chance of getting that combination
Part C: B is a dependent even due to the cards being drawn depending on the cards previously drawn. If you draw a Spade, then instead of a 13/52 chance, you have a 12/51 chance of drawing another spade. And etc. till you get to a 1/40 chance of getting a spade, if you, somehow, get 11 consecutive spades.
