Lacy draws a heart from a standard deck of 52 cards. Without replacing the first
ID: 3122132 • Letter: L
Question
Lacy draws a heart from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a diamond. Are these events independent? Input Yes or No: Determine the probability of drawing a heart and then a diamond without replacement. Write your answer in decimal form, rounded to four decimal places as needed.
Answer = Linda draws a heart from a standard deck of 52 cards
. She returns the heart to the deck, then draws a second card. Her second card is a diamond.
Are these events independent? Input Yes or No:
Determine the probability of drawing a heart and then a diamond with replacement.
Write your answer in decimal form, rounded to four decimal places as needed. Answer =
Explanation / Answer
In case of lacy the cards drawn without replacement are independent .
A pack of cards has 13 hearts and 13 diamonds
when a heart is drawn , probability P(Heart) = 13/52
the card is not replaced and diamond is drawn ,
now the total cards will be 51 because one card is already drawn
so P(diamond)= 13/ 51
total probability = 13/52 *13/51 =0.06372
In case of linda, the cards drawn with replacement are not independent .
A pack of cards has 13 hearts and 13 diamonds
when a heart is drawn , probability P(Heart) = 13/52
the card is now replaced and diamond is drawn ,
now the total cards will remain 52 because one card is drawn is returned back
so P(diamond)= 13/ 52
total probability = 13/52 *13/52 = 0.0625
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