Answer:18
Step-by-step explanation: 19-7=12 bolts and 7+7=14 so 12-14=18
If a sample of 7 bolts is selected, then the probability that all in the sample are defective = [tex]\frac{7}{50388}[/tex]
If a sample of 7 bolts is selected, then the probability that none in the sample are defective = [tex]\frac{66}{4199}[/tex]
"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
For given question,
Out of 19 bolts, 7 bolts are defective.
So 19 - 7 = 12 bolts are non-defective.
If sample of 7 bolts is selected.
The total number of ways of selecting 7 bolts from the 19 bolts.
Using combination formula,
[tex]^{19}C_7\\\\=\frac{19!}{7!(19-7)!} \\\\=50388[/tex]
Let event A: all bolts in the sample are defective
n(A) = 7
So the probability that all in the sample are defective would be,
[tex]P(A)=\frac{7}{50388}[/tex]
Let event B: no bolt in the sample are defective
This means the sample of 7 bolts has non-defective.
The total number of ways of selecting 7 bolts from the 12 non-defective bolts.
Using combination formula,
[tex]^{12}C_7\\=\frac{12!}{7!(12-7)!}\\\\ =792[/tex]
son n(B) = 792
So, the probability that none in the sample are defective would be,
[tex]P(B)=\frac{792}{50388} \\\\P(B)=\frac{66}{4199}[/tex]
Therefore, If a sample of 7 bolts is selected, then the probability that all bolts in the sample are defective = [tex]\frac{7}{50388}[/tex]
If a sample of 7 bolts is selected, then the probability that none in the sample are defective = [tex]\frac{66}{4199}[/tex]
Learn more about probability here:
brainly.com/question/11234923
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