Probability Problems

[popatpandu]

Questions 1, 2, and 3 are based on the joint probability table below for the events A, B, C and I, J.
I J Totals
A 0.07 0.03 0.1
B 0.40 0.10 0.5
C 0.33 0.07 0.4
Totals 0.80 0.20 1

1. Which of the following statements is true?
a. A and I are independent events
b. B and I are independent events
c. C and J are independent events
d. None of the above

2. Calculate P(B|I)
a. 0.50
b. 0.40
c. 0.20
d. 0.80

3. Calculate P(I|B)
a. 0.50
b. 0.40
c. 0.20
d. 0.80

4. A spy-in-training has to pass through two checkpoints before being sent on a mission. Each of the two checkpoints makes an independent check of his false documents and each has a 0.2 chance of detecting the spy. Again, assuming each check is independent, what is the probability that the spy will pass through both the checkpoints undetected?

a. 0.8
b. 0.64
c. 0.4
d. 0.36

Answer questions 5 and 6 using the following information: It is known that 80% of car owners in the US have insurance; the rest do not. Car owners under 30 years of age (Younger) are 25% of the population. Among Younger, 70% have insurance.

5. What is the probability that a randomly selected car owner is Older (30 or more years of age) and has no insurance?
a. 0.175
b. 0.075
c. 0.125
d. 0.15

6. If a randomly selected car owner has no insurance, what is the probability that he or she is Older?
a. 0.375
b. 0.0045
c. 0.15
d. 0.625
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[RonPurewal]

please follow the forum rules, including the following:

(1) post exactly one problem per thread

(2) title the thread using the first 6-8 words of the problem statement

(3) GIVE ATTRIBUTIONS for the problems (i.e., cite the source). if you don't do this, we'll simply delete the thread because of copyright issues.

thank you.

--

by the way, there is absolutely no way you'll see anything like #1, #2, or #3 on the gmat, and it is very unlikely indeed that you will see anything like #6.