Question

More cards! Consider again a standard deck of 52 cards (13 in each of 4 suits). Two cards are dealt in succession (meaning no replacement).

a) What is the probability that both cards are greater than 7 (assuming that the ace is considered “high” or greater than 7)?

b)Given that the first card was a queen, what is the probability that the second card is a seven?

c) What is the probability of being dealt a queen first followed by a seven?

d) What is the probability that both cards are greater than 7 (assuming that the ace is considered “high” or greater than 7)?

Answer 1

how many cards are greater than 7?

Answer 2

i count \(7\times 4=28\)
so the answer to the first one is
\[
\frac{28}{52}\times \frac{27}{51}\] whatever that is

Answer 3

Given that the first card was a queen, what is the probability that the second card is a seven
the first card is a queen
there are 4 sevens left, and 51 cards left
\[\frac{4}{51}\] for that one

Answer 4

So for the first one, would be 756/2652 ?

Answer 5

i don't know, i didn't do it

Answer 6

http://www.wolframalpha.com/input/?i=28*27%2F%2852*51%29

Answer 7

cancel first, multiply last

Answer 8

so 63/221 ?

Answer 9

that is what the wolf says, yes

Answer 10

okay so how would i do C now?

Answer 11

first card is a queen
what is the probability of that?

Answer 12

4/52 ?

Answer 13

is B and C asking the same thing?

Answer 14

no

Answer 15

i mean yes, \(\frac{4}{52}\) is right, but B and C are different questions

Answer 16

This is was i have so far
a) 63/221
b) 4/51
c)
d)

Answer 17

\(\frac{4}{52}\) is the probability that the first one is a queen
\(\frac{4}{51}\) is the probability that the second one is a 7 IF the first one is a queen
(that is why the denominator is 51 instead of 52)

Answer 18

to find your answer, multiply
\[\frac{4}{52}\times \frac{4}{51}\]

Answer 19

A and D are identical questions

Answer 20

1/663 for c???

Answer 21

im confused on C

Answer 22

lets go slow

Answer 23

ok thank you

Answer 24

the probability that the first card is a queen is
\[\frac{4}{52}=\frac{1}{13}\]

Answer 25

now you need the probability that the second card is a 7, given that the first card was a queen
because one queen is out of the deck, there are 51 cards left
of those 51 cards, 4 are sevens
that probability is \[\frac{4}{51}\]

Answer 26

yes so that is my answer to b? what is the difference in questions between b and c

Answer 27

to get the probability that the first is a queen AND the second is a seven, you multiply those two probabilities, i.e. compute
\[\frac{1}{13}\times \frac{4}{51}\]

Answer 28

that was the answer to C, not to B

Answer 29

so 4/663

Answer 30

ok
the purpose of question B, whose answer is \(\frac{4}{51}\) was to make you realize that the answer to C is \(\frac{1}{13}\times \frac{4}{51}\)

Answer 31

okay phew thank you, so this is what i have now:
a) 63/221
b) 4/51
c) 4/663
d) 63/221

Answer 32

unless there is a typo somewheres, A and D are identical questions
they look identical to you?

Answer 33

yes they look identical to me too, so i just put the same answer

Answer 34

thank you for helping me

Answer 35

yw

Answer 36

The A.P. Statistics exam consists of a multiple-choice section where each question has five choices. Sara estimates that she has a 75% chance of knowing each question. If she does not know the answer, she will randomly guess.

a) What is the probability of Sara getting a question correct?

b) The A.P. exam has 40 questions, how many might Sara expect to get correct?

Answer 37

any idea with this one?

Answer 38

@satellite73