1-4 The oasis outpost of Abu Ilan, in the heart of the Neveg dessert, has popula
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Question
1-4 The oasis outpost of Abu Ilan, in the heart of the Neveg dessert, has population of 24 Bedouin tribesmen and 16 Farima tribesman. El Kamin, a nearby oasis, has a population of 8 Bedouin s and 36 Farima. A lost Israeli soldier, accidently separated from his Army unit, is wandering through the desert and arrives at the edge of one of the oases. The soldier has no idea which oasis he has found, but the first person he spots at distance is a Bedouin.
a.What is the probability that he wandered into Abu Ilan?
b.What is the probability he is in El Kamin?
1-5 In a sample of 1,000 representing a survey from the entire population, 600 people were from Laketown and the rest were from River City. Of the sample, 19 had some form of cancer. Twelve of those were from Laketown.
a.Are the events of living in Laketown and having cancer of some sort of cancer independent?
b.Which city would you prefer to live in, assuming that your main objective was to avoid having cancer?
1-6 Gary Schwartz is the top salesman for his company. Records indicate that he makes a sale on 70% of his sales calls.
a.If he calls on 6 potential clients, what is the probability he makes exactly 4 sales?
b.What is the probability he make fewer than 3 sales?
Explanation / Answer
1-4
Tribes
Bedouin
Farima
Total
Abu Ilan
24
16
40
El Kamin
8
36
44
Total
32
52
Probability of spot a Bedouin @ Abu Ilan = 24/32 = 75%
Probability of spot a Bedouin @ El Kamin = 8/32 = 25%
75% probability that the soldier wander in Abu Ilan and 25% in El Kamin
1-5
Total Population (n) = 1000
Population@ Laketown = 600
Population @ River city = 400
Total population having cancer = 19
Total population having cancer @ Laketown = 12
Probability of having cancer = 19/1000 = 1.9%
Probability of having cancer @ Laketown = 12/600 = 2%
Probability of having cancer @ River city = 7/400 = 1.75%
The events are independent as the total probability is 1.9% overall
Would like to prefer River city as probability of having cancer is less.
1-6
Probability of success (p) = 0.7
Probability of failure (q) = 0.3
No. of trials (n) = 6
P(x) = n! / x! (n-x)! * pn * q (n-x)
a. If he calls on 6 potential clients, what is the probability he makes exactly 4 sales?
If P(x=4)
= 6! / 4! (6-4)! * (0.7)4 * (0.3)2
= 15 * 0.2401 * 0.09
P(x=4) = 0.3241
b. What is the probability he make fewer than 3 sales?
If P(x<3), can be simplified to = P(x=0) + P(x=1) + P(x=2)
Using above formula, you can arrive
P(x=0) = 0.000729
P(x=1) = 0.010206
P(x=2) = 0.059535
P(x<3) = 0.07047
Tribes
Bedouin
Farima
Total
Abu Ilan
24
16
40
El Kamin
8
36
44
Total
32
52
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