MATHEMATICS COLLEGE

Imagine you and Janice are the only ones working as telemarketers for a large cooperation. You make 70% of the calls and each call takes you Exponential amount of time with parameter λ1 = 2 hrs-1 . Janice, on the other hand, makes the remaining 30% of total calls. Each call takes her Exponential amount of time with parameter λ2 = 4 hrs-1 . A certain call was made 30 minutes ago and it is still ongoing. What is the probability that you made this call?

Answers

Answer 1

Answer:

Answer:

The probability that you made this call is 0.8639.

Explanation:

Parameter for you = λ1 = 2

⇒ β1 = 1 / λ1 = 1 / 2 = 0.5

Parameter for Janice = λ2 = 4

⇒ β2 = 1 / λ2 = 1 / 4 = 0.25

Probability that you made a for 0.5 hours or more:

$P(X\geq 0.5)=e^(-0.5/0.5)=0.3679$

Probability that Janice made a for 0.5 hours or more:

$P(X\geq 0.5)=e^(-0.5/0.25)=0.1353$

Overall probability that a call was made for 0.5 hours of more

= (0.7 x 0.3679) + (0.3 x 0.1353)

= 0.2981

Probability that you made the given call

= 0.7 x 0.3679 / 0.2981

= 0.8639

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Answers

Answer:

a) 0.73684

b) 2/3

Step-by-step explanation:

part a)

$P ( A is 1 / exactly two balls are 1) = (P ( A is 1 and that exactly two balls are 1))/(P (Exactly two balls are one))$

Using conditional probability as above:

(A,B,C)

Cases for numerator when:

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= $((1)/(6)* (11)/(12)*(1)/(4)) + ((1)/(6)*(1)/(12)*(3)/(4)) = 0.048611111$

Cases for denominator when:

P( Exactly two balls are 1) = P( 1, not 1, 1) + P(1, 1, not 1) + P(not 1, 1 , 1)

$= ((1)/(6)* (11)/(12)*(1)/(4)) + ((1)/(6)*(1)/(12)*(3)/(4)) + ((5)/(6)*(1)/(12)*(1)/(4))= 0.0659722222$

Hence,

$P ( A is 1 / exactly two balls are 1) = (P ( A is 1 and that exactly two balls are 1))/(P (Exactly two balls are one)) = (0.048611111)/(0.06597222) \n\n= 0.73684$

Part b

$P ( B = 12 / A+B+C = 21) = (P ( B = 12 and A+B+C = 21))/(P (A+B+C = 21))$

Cases for denominator when:

P ( A + B + C = 21) = P(5,12,4) + P(6,11,4) + P(6,12,3)

$= 3*P(5,12,4 ) =3* (1)/(6)*(1)/(12)*(1)/(4)\n\n= (1)/(96)$

Cases for numerator when:

P (B = 12 & A + B + C = 21) = P(5,12,4) + P(6,12,3)

$= 2*P(5,12,4 ) =2* (1)/(6)*(1)/(12)*(1)/(4)\n\n= (1)/(144)$

Hence,

$P ( B = 12 / A+B+C = 21) = ((1)/(144) )/((1)/(96) )\n\n= (2)/(3)$

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Answers

Answer:

Step-by-step explanation:

(●'◡'●)

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

Answer:

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Answers

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Answers

Answer:

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Answer:

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