Question

Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a spade.
Are these events independent?
Input Yes or No:

Determine the probability of drawing a diamond and then a spade without replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =

Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a spade.

Are these events independent?
Input Yes or No:
Determine the probability of drawing a diamond and then a spade with replacement.
Write your answer in decimal form, rounded to four decimal places as needed.
Answer =

Answer 1

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade  = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement  is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond  = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade  = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625