suppose that 90% of bolts and 85% of nails meet specifications. one bolt and one nail are chosen independently.
a. what is the probability that both meet specifications?
b. what is the probability that neither meet specifications?
c. what is the probability that at least one of them meets specification?
Answers
Step-by-step explanation:
A 90% probability that a bolts meets
specifications
A 85% probability that a nail meets
specifications.
What is the probability that both meet
specifications?
We multiply both probabilities:
0.9*0.85 = 0.765
76.5% probability that both meet specifications.
What is the probability that neither meets
specifications?
A 10% probability that a bolts does not meet
specifications
A 15% probability that a nail does not meet
specifications.
0.1*0.15 = 0.015
1.5% probability that neither meets
specifications
What is the probability that at least one of
them meets specifications?
Either neither meets specifications, or at
least one of them does. The sum of these
probabilities is 100%.
From the second question, 1.5% probability that
neither meets specifications.
So 100-1.5 = 98.5% probability that at least one
Answer:
(a). 76.5% probability that both meet specifications.
(b). 1.5% probability that neither meets specifications.
(c). 98.5% probability that at least one.
Step-by-step explanation:
(a). We multiply both probabilities:
0.9*0.85 = 0.765
76.5% probability that both meet specifications.
(b). A 10% probability that a bolts does not meet specifications
A 15% probability that a nail does not meet specifications.
0.1*0.15 = 0.015
1.5% probability that neither meets specifications.
(c). Either neither meets specifications or at least one of them does. The sum of these probabilities is 100%.
From the second question, 1.5% probability that
neither meets specifications.
So
100-1.5 = 98.5
98.5% probability that at least one.