1. A travel agency surveyed 125 potential customers. The following information w

Question

1. A travel agency surveyed 125 potential customers. The following information was obtained: 68 wished to travel to Hawaii, 53 wished to travel to Las Vegas, and 47 wished to travel to Orlando. Moreover, 34 wished to travel to Hawaii and Las Vegas, 26 wished to travel to Las Vegas and Orlando, 23 wished to travel to Hawaii and Orlando, and finally, 18 wished to travel to all three top destinations. Answer the following questions using the provided Venn diagram.

I completed the Venn diagram and the answer I got was but I do not understand the rest can someone please help and explain this to me. Please

N(U) = 125 Universal (U)
N(A) = 68   Hawaii (A)
N(B) = 53   Las Vegas (B)
N(C) = 47   Orlando (C)
N(A and B) = 34
N (B and C) = 26
N (A and C) = 23
N([A and B) and C] =18

(a) If you select a customer at random, what is the probability that the selected customer wanted to travel to none of the top three destinations mentioned? 22 out of 125

(b) If you select a customer at random, what is the probability that the selected customer wanted to travel to Orlando and Las Vegas, but not Hawaii?

(c) If you select a customer at random, what is the probability that the selected customer wanted to travel to Orlando or Las Vegas, but not Hawaii? (d) If you select a customer at random, what is the probability that the selected customer wanted to travel to exactly two of the top three destinations mentioned in the problem? (e) If you select a customer at random, what is the probability that the selected customer wanted to travel to at least two of the top three destinations mentioned in the problem? 47 out of 125

2. An insurance company surveyed 150 drivers. The survey showed that 115 drivers had no accident for at least one year, 46 had at least one traffic violation this past year, and 21 drivers surveyed had at least one violation and an accident this past year. Answer the following questions. Drawing a Venn diagram may be help.

(a) If a driver is selected at random, what is the probability that the selected driver had no violation and no accident this past year?

(b) If a driver is selected at random, what is the probability that he/she had no traffic violation this past year but had an accident?

Explanation / Answer

selected wanted to go none of the 3 destinations N(AUBUC)c =125-P(wants to go at least one of them)=125-N(AUBUC)

=125-(N(A)+N(B)+N(C)-N(AnB)-N(BnC)-PN(CnA)+P(AnBnC)) =22

a)hence  probability that the selected customer wanted to travel to none of the top three destinations mentioned=22/125

b)probability that the selected customer wanted to travel to Orlando and Las Vegas, but not Hawaii

=(N(BnC)-N(AnBnC))/125=(26-18)/125 =8/125

c)probability that the selected customer wanted to travel to Orlando or Las Vegas, but not Hawaii

=(N(AUBUC)-N(A))/125 =(103-68)/125 =35/125

d)probability that the selected customer wanted to travel to exactly two of the top three destinations mentioned in the problem =(N(AnB)+N(BnC)+N(CnA)-3*N(AnBnC))/125 =(34+26+23-3*18)/125=29/125

e)probability that the selected customer wanted to travel to at least two of the top three destinations mentioned in the problem=(N(AnB)+N(BnC)+N(CnA)-2*N(AnBnC))/125=(34+26+23-2*18)/125=47/125

2)number of no accidents =N(Ac) =115 ; Number of atleast one accidents =P(A) =150-115=35

at least one traffic violation =N(T) =46 ; number of no traffic violation =N|(Tc) =150-46=104

at least one violation and an accident this past year =N(TnA) =21

here people with at least no accident or no traiffic violation =N(AcUTc) =150-21 =129

a) probability that the selected driver had no violation and no accident this past year=(N(Ac)+N(Tc)-N(AcUTc))/150

=(115+104-129)/150=90/150

b) probability that he/she had no traffic violation this past year but had an accident=(35-21)/150=14/150

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