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
