Three playing cards – a jack, a queen, and a king – are placed in a box. A card is drawn from the box, its value is recorded, and then the card is put back into the box. The process is then repeated a second time.
a) Determine the number of outcomes in which a king is the first card drawn from the box.
b) Find the probability that the first and second cards drawn are the same
2007-06-26 03:55:01 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
a) There are 9 total outcomes (3 different first cards * 3 different second cards):
KK KQ KJ
QK QQ QJ
JK JQ JJ
Of those nine, three (KK KQ KJ) have a king as the first card.
b) Of the 9 total outcomes, 3 (KK QQ JJ) have the second card the same as the first. 3/9 = 1/3 is the probability that the second card will be the same.
2007-06-26 03:59:19 · answer #1 · answered by McFate 7 · 1⤊ 0⤋
a. The probability is one in three. There are always three cards, there will always be the chance of one in three.
b. The probability is again, one in three. for the same reason.
This is rather like "what is the probability that after a couple has had five children all boys, what is the probability that the sixth child will be a girl?" the chances are 50-50 for each birth. However, if you were a betting person, since the father has sired only boys, I'd be betting that the next one would be a boy as well, even tho the probability is still 50-50.
This is what probability is. However the father might be tested to see just how many of his sperm carried the gene for maleness, and how mobile those sperm were. Probability with cards is far easier.
2007-06-26 04:05:49 · answer #2 · answered by April 6 · 1⤊ 0⤋
a)
king is one of three cards that might be drawn. so probability of king being drawn in first draw = 1/3 or 33%
b)
it can be either both K or both Q or both J. since card is being replaced after each draw, at each draw the probabiity of a specific card being drawn is same at 1/3
reqd prob = (1/3)*(1/3) + (1/3)*(1/3) + (1/3)*(1/3)
= 1/9 + 1/9 + 1/9
= 3/9
=1/3
2007-06-26 04:03:13 · answer #3 · answered by Vipin A 3 · 0⤊ 0⤋
a) 1/3
b) 3/3 x 1/3 = 1/3
Since the first card doesnt matter. (You can pick up K Q or J).
But the second time you pick up the card does, because you want to get the same card. And you have a third of a chance to pick up the same card. (Because there is J K Q, only one of them is the one you want.)
Assuming only three cards the box.
2007-06-26 04:04:31 · answer #4 · answered by Anonymous · 0⤊ 0⤋
a) = 1/3
b) = 1/3
2007-06-26 04:01:28 · answer #5 · answered by maussy 7 · 0⤊ 0⤋
a)
K,K
K,Q
K,J
Q,Q
Q,K
Q,J
J,K
J,Q
J,J
3 Is the number of outcomes in which a king is the first card drawn from the box
b) P(second cards drawn are the same)=3/9=1/3.
2007-06-26 04:03:04 · answer #6 · answered by Anonymous · 0⤊ 0⤋
a. 2
b. 1/3 x 1/3= 1/9
Boy if this isn't a vague question, I don't know what is. It is not clear at all to know exactly what the question is asking.
2007-06-26 04:00:22 · answer #7 · answered by Noncyclicphotophosphorylation 2 · 0⤊ 1⤋
is it 100 - 1.805%
2007-06-26 03:59:15 · answer #8 · answered by d_champz_here 2 · 0⤊ 2⤋