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edjiejwi
15.08.2020 •
Mathematics
g 3.24 Socks in a drawer. In your sock drawer you have 4 blue, 5 gray, and 3 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing (a) 2 blue socks (b) no gray socks (c) at least 1 black sock (d) a green sock (e) matching socks
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Ответ:
Using the hypergeometric distribution, it is found that there is a:
a) 0.0909 = 9.09% probability that you end up with 2 blue socks.
b) 0.3182 = 31.82% probability that you end up with no gray socks.
c) 0.4545 = 45.45% probability that you end up with at least 1 black sock.
d) 0% probability that you end up with a green sock.
e) 0.2879 = 28.79% probability that you end up with matching socks.
Hypergeometric distribution:
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There is a total of 4 + 5 + 3 = 12 socks, henceItem a:
4 are blue, henceThe probability is P(X = 2), hence:
0.0909 = 9.09% probability that you end up with 2 blue socks.
Item b:
5 are gray, henceThe probability is P(X = 0), hence:
0.3182 = 31.82% probability that you end up with no gray socks.
Item c:
3 are black, henceThe probability is:
In which
0.4545 = 45.45% probability that you end up with at least 1 black sock.
Item d:
There are no green socks, hence 0% probability that you end up with a green sock.
Item e:
0.0909 probability of two blue.The probability of two gray is P(X = 2) when k = 5.The probability of two black is P(X = 2) when k = 3.Hence, for two gray:
Then, for two black:
Then, the probability of matching socks is:
0.2879 = 28.79% probability that you end up with matching socks.
A similar problem is given at link
Ответ:
a) 1/11 (b) 7/22 (c) 5/11 (d) 0 (e) 19/66
Step-by-step explanation:
Given the following :
Number of Blue socks = n(B) = 4
Number of Gray socks = n(G) =5
Number of black socks = n(Bl) = 3
Total number of socks = (4 + 5 + 3) = 12
Probability = ( number of required outcomes / number of total possible outcomes)
Picking 2 socks at random:
A) probability of two blue socks :
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(2 blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
B) No gray socks :
Number of non - gray socks = (4 + 3) = 7
1st pick = 7/12
After 1st pick non-gray socks left = 6
Total socks left = 11
2nd pick = 6 / 11
P(non-gray) = (7/12 × 6/11) = 42/132 = 7/22
C.) Atleast one black socks = (1 - P(no black))
Number of non-black socks = (4 +5) = 9
1st pick = 9/12 = 3/4
After 1st pick, non-black left = 8, total = 11
2nd pick = 8/11
P(non - black) = (3/4 × 8/11) = 24/44 = 6/11
P(atleast 1 black) = (1 - 6/11) = 5 /11
D.) A green socks
Number of green socks = 0
P(green) = 0
E.) A matching socks :
1) matching black socks :
Ist pick = p(Bl) = (3/12) = 1/4
Number of Black socks left = (3 - 1) =2
Total socks left = 12 - 1 = 11
2nd pick = p(Bl) = (2/11)
P(matching black socks) = (1/4 * 2/11) = 2 /44 = 1/22
11) matching blue socks:
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(matching blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
111) matching gray socks :
Ist pick = p(B) = (5/12) = 5/12
Number of Blue socks left = (5 - 1) =4
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (4/11)
P(matching gray socks) = (5/12 * 4/11) = 20/132 = 5 /33
Summing the probabilities :
(1/22 + 1/11 + 5/33) = (3 + 6 + 10) / 66 = 19/66
Ответ:
Step-by-step explanation:
We are solving for the number of students in each bus, so let x represent the number of students in each bus.
We have 4 + 9x = 472.
=> 9x = 468, x = 52.
Hence there are 52 students on each bus.