Worksheet 7
Worksheet 7
Worksheet 7
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<strong>Worksheet</strong> 7<br />
22s:008 Xiao Yang<br />
1. In the US, 70% of adults have health insurance. If 5 adults are randomly selected,<br />
(a) Find the probability none have health insurance.<br />
(b) Find the probability that at least one has health insurance.<br />
(c) Find the probability 4 or less have health insurance.<br />
2. A small factory has two bottling machines, namely, machine A and machine B. The bottles produced need to be<br />
examined to see whether they meet the requirements. Following table is the summary of production information over<br />
Feb. 2006.<br />
Rejected Accepted<br />
Machine A 50 950<br />
Machine B 100 2900<br />
(a) What proportion of bottles is rejected in Feb. 2006?<br />
(b) What proportion of bottles is produced by Machine A in Feb. 2006?<br />
(c) Find the probability that a randomly chosen bottle is rejected and is from machine A.<br />
(d) What is the probability that a randomly selected bottle is from Machine A, given that it is rejected?<br />
(e) Repeat (d) using the general product rule.<br />
(f) If a bottle is chosen at random, find the probability that it’s rejected and is from machine A. Using general<br />
product rule.<br />
(g) Given a bottle is from machine B, find the probability that it is accepted.
(h) Repeat (g) using the definition of conditional probability.<br />
(i) Find the probability that a bottle from machine B given it’s accepted. Using the definition of conditional<br />
probability.<br />
(j) Given a bottle is accepted, find the probability that it’s from machine A.<br />
(k) Repeat (j) using the definition of conditional probability.<br />
(l) Given that a bottle is rejected, find the probability that it’s from machine B.<br />
3. Automobiles use semiconductor chips for engine and emission control, repair diagnosis, and other purposes. An auto<br />
manufacturer buys chips from a supplier. The supplier sends shipments of semiconductors, of which 5% fail to function<br />
properly. Each automobile uses 12 chips, and each chip works independently of the others. What is the percentage of cars<br />
have problems with the chips?<br />
4. Suppose a bowl has four chips: two of the chips are black, and two of the chips are red. One of the black chips has the<br />
number 1 written on it, while the other black chip has the number 2 written on it. One of the red chips has the number 2<br />
written on it, while the other red chip has the number 3 written on it. Suppose one chip is randomly chosen from the bowl.<br />
Consider the following events: A= a black chip is chosen. B = the number on the chip is 2.<br />
(a) What is P(B|A)?<br />
(b) Are A, B independent? Why?<br />
(c) What is P(A or B)?
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