Respuesta :
A) The probability of picking a white tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
B) The probability of picking a blue tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
C) The probability of picking a red tie 300 times = [tex](\frac{1}{4}) ^{300}[/tex]
D) the probability of picking a black tie 300 times = [tex](\frac{3}{8}) ^{300}[/tex]
E ) the probability of picking a maroon tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
F) the probability of NOT picking a white tie 300 times = [tex](\frac{7}{8}) ^{300}[/tex]
Step-by-step explanation:
Here, the total number of black neckties = 6
The total number of white neckties = 2
The total number of red neckties = 4
The total number of maroon neckties = 2
The total number of blue neckties = 2
The number of times the experiment is repeated = 300
A ) P(Picking a white tie) = [tex]\frac{\textrm{Total number of white ties}}{\textrm{Total Bow ties}}[/tex]
= [tex]\frac{2}{16} = \frac{1}{8}[/tex]
So, the probability of picking a white ONCE is 1/8.
Now, as the experiment is REPEATED 300 times with replacement.
So, the probability of picking a white tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
B) P(Picking a BLUE tie) = [tex]\frac{\textrm{Total number of blue ties}}{\textrm{Total Bow ties}} = \frac{2}{16} = \frac{1}{8}[/tex]
So, the probability of picking a blue ONCE is 1/8.
Hence, the probability of picking a blue tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
C) P(Picking a Red tie) = [tex]\frac{\textrm{Total number of Red ties}}{\textrm{Total Bow ties}} = \frac{4}{16} = \frac{1}{4}[/tex]
So, the probability of picking a red ONCE is 1/4.
Hence, the probability of picking a red tie 300 times = [tex](\frac{1}{4}) ^{300}[/tex]
D) P(Picking a Black tie) = [tex]\frac{\textrm{Total number of black ties}}{\textrm{Total Bow ties}} = \frac{6}{16} = \frac{3}{8}[/tex]
So, the probability of picking a red ONCE is 3/8.
Hence, the probability of picking a black tie 300 times = [tex](\frac{3}{8}) ^{300}[/tex]
E) P(Picking a maroon tie) = [tex]\frac{\textrm{Total number of maroon ties}}{\textrm{Total Bow ties}} = \frac{2}{16} = \frac{1}{8}[/tex]
So, the probability of picking a maroon ONCE is 1/8.
Hence, the probability of picking a maroon tie 300 times = [tex](\frac{1}{8}) ^{300}[/tex]
F) P(Picking a NOT whiten tie) = 1 - P( picking a white tie)
[tex]= 1-(\frac{1}{8} ) = \frac{8-1}{8} = (\frac{7}{8} )[/tex]
So, the probability of NOT picking a white ONCE is 7/8.
Hence, the probability of NOT picking a white tie 300 times = [tex](\frac{7}{8}) ^{300}[/tex]
Using the binomial distribution, it is found that the expected values are given by:
A. 37.5.
B. 37.5.
C. 75
D. 112.5.
E. 37.5.
F. 262.5.
What is the binomial probability distribution?
It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this problem, the trial is repeated 300 times, hence n = 300.
Item a:
2 out of 16 neckties are white, hence: p = 2/16.
The expected value is given by:
E(X) = 300 x 2/16 = 37.5.
Item b:
2 out of 16 neckties are blue, hence: p = 2/16.
The expected value is given by:
E(X) = 300 x 2/16 = 37.5.
Item c:
4 out of 16 neckties are red, hence: p = 4/16.
The expected value is given by:
E(X) = 300 x 4/16 = 75.
Item d:
6 out of 16 neckties are black, hence: p = 6/16.
The expected value is given by:
E(X) = 300 x 6/16 = 112.5.
Item e:
2 out of 16 neckties are maroon, hence: p = 2/16.
The expected value is given by:
E(X) = 300 x 2/16 = 37.5.
Item f:
14 out of 16 neckties are not white, hence: p = 14/16.
The expected value is given by:
E(X) = 300 x 14/16 = 262.5.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
