The person is frequently or occasionally involved in chanty wink the person is f
ID: 3177605 • Letter: T
Question
The person is frequently or occasionally involved in chanty wink the person is female or not involved in chanty work at all the person is male or frequently involved in charity work the person in female or not frequently involved in charity work. the table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample Find the probability of each event. the person wears only contacts or only glasses. the person is male or wears both contacts and glasses. the person is female or wears neither contacts nor glasses. the person is male or does not wear glasses.Explanation / Answer
(a)
number of person wears contacts, n(C) = 253
number of person wears glasses, n(G) = 1268
number of person wears both, n(CG) = 545
number of person wears neither, n(C'G') = 1137
P(C) = 253/3203 = 0.079
P(G) = 1268/3203 = 0.3959
P(CG) = 545/3203 = 0.1702
required probability, P(C or G) = 0.079 + 0.3959 = 0.4749
(b)
probability person is male, P(M) = 1538/3203 = 0.4802
probability a person wears both contacts and glasses, P(CG) = 0.1702
Probability person is male and wears both contacts and glasses, P(MCG) = 177/3203 = 0.0553
Probability person is male or wears both contacts and glasses = P(M) + P(CG) - P(MCG) = 0.4802 + 0.1702 - 0.0553 = 0.5951
(c)
probability person is female, P(F) = 1665/3203 = 0.5198
probability a person wears neither contacts nor glasses, P(C'G') = 1137/3203 = 0.355
Probability person is female and wears neither contacts nor glasses, P(FC'G') = 681/3203 = 0.2126
Probability person is female or wears neither contacts nor glasses = P(F) + P(C'G') - P(FC'G') = 0.5198 + 0.355 - 0.2126 = 0.6622
(d)
Probability that a person is male P(M) = 1538/3203 = 0.4802
Probability that a person does not wear glasses P(G') = (3203-1268-545)/3203 = 0.434
Probability that a person is male and does not wear glasses, P(MG') = (1538-841-177)/3203 = 0.1624
Required probability = 0.4802 + 0.434 - 0.1624 = 0.7518
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