Problems Probability Models Worksheets Page 7
Download a blank fillable Problems Probability Models Worksheets in PDF format just by clicking the "DOWNLOAD PDF" button.
Open the file in any PDF-viewing software. Adobe Reader or any alternative for Windows or MacOS are required to access and complete fillable content.
Complete Problems Probability Models Worksheets with your personal data - all interactive fields are highlighted in places where you should type, access drop-down lists or select multiple-choice options.
Some fillable PDF-files have the option of saving the completed form that contains your own data for later use or sending it out straight away.
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
2
4
b) P(a Type AB donor among the first 5 people checked) =
0 04
0 96 0 04
0 96
0 04
0 96
0 04
0 185
.
.
.
.
.
...
.
.
.
2
5
c) P(a Type AB donor among the first 6 people checked) =
0 04
0 96 0 04
0 96
0 04
0 96
0 04
0 217
.
.
.
.
.
...
.
.
.
9
d) P(no Type AB donor before the 10th person checked) = P(X > 9) =
0 96
0 693
. This one is a bit tricky. There is no
.
.
implication that we actually find a donor on the 10th trial. We only care that nine trials passed with no Type AB donor.
12. These may be considered Bernoulli trials. There are only two possible outcomes, colorblind and not colorblind. As long as the
men selected are representative of the population of all men, the probability of being colorblind is constant at about 8%. Trials are
not independent, since the population is finite, but we won’t be sampling more than 10% of the population.
Let X = the number of people checked until the first colorblind man is found. Since we are selecting people until the first success,
the model Geom(0.08), may be used.
1
1
a)
12 5
people. We expect to examine 12.5 people until finding the first colorblind person.
E x
.
0 08
p
.
4
b) P(no colorblind men among the first 4) = P(X > 4) =
0 92
0 716
.
.
5
c) P(first colorblind man is the sixth man checked) = P(X = 6) =
0 92
0 08
0 0527
.
.
.
2
8
d) P(she finds a colorblind man before the tenth man) =
0 08
0 92 0 08
0 92
0 08
0 92
0 08
0 528
.
.
.
.
.
...
.
.
.
13. These may be considered Bernoulli trials. There are only two possible outcomes, lefthanded and not left-handed. Since people are
selected at random, the probability of being left-handed is constant at about 13%. The trials are not independent, since the
population is finite, but a sample of 5 people is certainly fewer than 10% of all people.
Let X = the number of people checked until the first lefty is discovered.
Let Y = the number of lefties among n = 5.
4
a) P(first lefty is the fifth person) = P(X = 5) =
0 87
0 13
0 0745
.
.
.
5
0
5
b) P(some lefties among the 5 people) = 1 − P(no lefties among the first 5 people) =
1
0 13
0 87
0 502
.
.
.
0
2
c) P(first lefty is second or third person) = P(X = 2) + P(X = 3) =
0 87 0 13
0 87
0 13
0 211
.
.
.
.
.
5
3
2
d) P(exactly 3 lefties in the group ) =
0 13
0 87
0 0166
.
.
.
3
5
5
5
3
2
4
1
5
0
e) P(at least 3 lefties in the group) =
0 13
0 87
0 13
0 87
0 13
0 87
0 0179
.
.
.
.
.
.
.
3
4
5
5
5
0
5
3
2
f) P(at most 3 lefties in the group) =
0 13
0 87
0 13
0 87
0 9987
.
.
...
.
.
.
0
3
14. These may be considered Bernoulli trials. There are only two possible outcomes, hitting the bull’s-eye and not hitting the bull’s-
eye. The probability of hitting the bull’s-eye is given, p = 0.80. The shots are assumed to be independent.
Let X = the number of shots until the first bull’s-eye.
Let Y = the number of bull’s-eyes in n = 6 shots.
6
2
6
0
a)
0 2
0 8
0 032
b)
1
0 8
0 2
0 738
.
.
.
.
.
.
6
6
3
4
4
2
c)
0 2
0 8
0 2
0 8
0 00768
d)
0 8
0 2
0 246
.
.
.
.
.
.
.
.
4
6
6
6
6
6
4
2
5
1
6
0
0
6
4
2
e)
0 8
0 2
0 8
0 2
0 8
0 2
0 901
f)
0 8
0 2
0 8
0 2
0 345
.
.
.
.
.
.
.
.
.
...
.
.
.
4
5
6
0
4
15. a) E(Y) = np = 5(0.13 ) = 0.65 lefties.
b) SD(Y) =
5 0 13 0 87
0 75
lefties
npq
.
.
.
1
1
c) Let X = the number of people checked until the first lefty is discovered.
7 69
people
E x
.
0 13
p
.
16. a) E(Y) = np = 6(0.8) = 4.8 bull’s-eyes
6 0 8 0 2
0 98
b) SD(Y) =
bull’s-eyes
npq
.
.
.
1
1
c) Let X = the number of arrows shot until the first bull’s-eye
1 25
shots
E x
.
0 8
p
.
17. a) E(Y) = np = 12(0.87) = 10.44 righties. SD(Y) =
12 0 87 0 13
1 16
righties
npq
.
.
.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education