SOLUTION: 1.(a) Kara needs to pick a pair of matching socks from a drawer consisting of 4 black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first sock that Kara draws is

Algebra ->  Probability-and-statistics -> SOLUTION: 1.(a) Kara needs to pick a pair of matching socks from a drawer consisting of 4 black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first sock that Kara draws is      Log On


   

Question 1157048: 1.(a) Kara needs to pick a pair of matching socks from a drawer consisting of 4
black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first sock
that Kara draws is blue, what is the probability that she will get a matching
sock on her second draw?
(b) If Sam's closet contains blue and green shirts. He has eight blue shirts and
seven green shirts. Five of the blue shirts have stripes, and four of the green
shirts have stripes. What is the probability that Sam randomly chooses a shirt
that is blue or has stripes?
(c) At a birthday party, there are 3 gift boxes that are red, 7 gift boxes that
are green, 4 gift boxes that are blue, and 10 gift boxes that are multi-colored
sitting on a table. If one of the gift boxes falls off the table at random, what
is the probability that the gift box will be green?
Found 3 solutions by VFBundy, ikleyn, Edwin McCravy:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
1.(a) Kara needs to pick a pair of matching socks from a drawer consisting of 4 black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first sock that Kara draws is blue, what is the probability that she will get a matching sock on her second draw?

21/45

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(b) If Sam's closet contains blue and green shirts. He has eight blue shirts and seven green shirts. Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the probability that Sam randomly chooses a shirt that is blue or has stripes?

8/15 + 9/15 - 5/15 = 12/15 = 4/5

==============================================================

(c) At a birthday party, there are 3 gift boxes that are red, 7 gift boxes that are green, 4 gift boxes that are blue, and 10 gift boxes that are multi-colored sitting on a table. If one of the gift boxes falls off the table at random, what is the probability that the gift box will be green?

7/24

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Here I present another version of the solution and the answer to part  (a).


From the context,  my understanding of part  (a)  is that 

    There are 4 separate black socks in the drawer (not 4 pairs of black socks, as the tutor @VFBundy assumes);

    There are 11 separate blue socks in the drawer (not 11 pairs of blue socks, as the tutor @VFBundy assumes);

    There are 3 separate white socks in the drawer (not 3 pairs of white socks, as the tutor @VFBundy assumes);

    There are 5 separate brown socks in the drawer (not 5 pairs of black socks, as the tutor @VFBundy assumes).

Then the solution and the answer are 

    P = %2811-1%29%2F%284%2B%2811-1%29%2B3%2B5%29 = 10%2F22 = 5%2F11.    ANSWER


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1.(a) Kara needs to pick a pair of matching socks from a drawer consisting of
4 black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first
sock that Kara draws is blue, what is the probability that she will get a
matching sock on her second draw?

21/45
That answer is incorrect.  In the beginning there were 4+11+3+5=23 socks in the
drawer, 11 of them blue. We are told that she has already drawn a blue sock.  So
now there are only 22 socks left in the drawer, of which now only 10 of them are
blue. Therefore, the probability that she will draw one of the 10 remaining blue
socks out of the 22 remaining socks is 10 out of 22 or 10/22 which reduces to
5/11.


==============================================================

(b) If Sam's closet contains blue and green shirts. He has eight blue shirts
and seven green shirts. Five of the blue shirts have stripes, and four of the
green shirts have stripes. What is the probability that Sam randomly chooses a
shirt that is blue or has stripes?

8/15 + 9/15 - 5/15 = 12/15 = 4/5

That is correct but here is a better (I think!) way to explain it.  Make this
chart, filling in the numbers we are given:

       ------------------------------------ 
       | STRIPES  | NO STRIPES  || TOTALS |
-------------------------------------------
BLUE   |    5     |             ||   8    | 
-------------------------------------------
GREEN  |    4     |             ||   7    |
===========================================
TOTALS |          |             ||        |
------------------------------------------- 

Now we can fill in the number of BLUE shirts with NO STRIPES by subtracting 
8-5=3.

We can fill in the number of GREEN shirts with NO STRIPES by subtracting 7-4=3.


We can fill in the TOTAL shirts by adding 8+7=15:

       ------------------------------------ 
       | STRIPES  | NO STRIPES  || TOTALS |
-------------------------------------------
BLUE   |    5     |      3      ||   8    | 
-------------------------------------------
GREEN  |    4     |      3      ||   7    |
===========================================
TOTALS |          |             ||  15    |
------------------------------------------- 

Now we can fill in the totals by adding 5+4=9 and 3+3=6:

       ------------------------------------ 
       | STRIPES  | NO STRIPES  || TOTALS |
-------------------------------------------
BLUE   |    5     |      3      ||   8    | 
-------------------------------------------
GREEN  |    4     |      3      ||   7    |
===========================================
TOTALS |    9     |      6      ||  15    |
------------------------------------------- 

Now the probability that Sam randomly chooses a shirt that is blue or has
stripes are the ones I have made red below:

       ------------------------------------ 
       | STRIPES  | NO STRIPES  || TOTALS |
-------------------------------------------
BLUE   |    5     |      3      ||   8    | 
-------------------------------------------
GREEN  |    4     |      3      ||   7    |
===========================================
TOTALS |    9     |      6      ||  15    |
------------------------------------------- 

So that's 5+3+4=12 out of the 15, or 12/15, which reduces to 4/5.

==============================================================

(c) At a birthday party, there are 3 gift boxes that are red, 7 gift boxes
that are green, 4 gift boxes that are blue, and 10 gift boxes that are multi-colored sitting on a table. If one of the gift boxes falls off the table at
random, what is the probability that the gift box will be green?

7/24
That is correct. There are 3+7+4+10=24 gift boxes. Therefore the probability
that the gift box that fell off the table will be green is 7 out of the 24 or
7/24.

Edwin