Question

13) you collect playing cards for a popular monster battling game. There are four types of cards each with a different value. You have a ½ chance of getting a common card which is worth dollar 0.50. uncommon cards only occur 3/10 and are worth $1 rare cards occur 3/20 and are worth $5Ultra rare cards occur 1/20 and are worth $10. What is the expected value of a single card? What is E(300X+2)?

1) The school bus has the same probability of arriving any time between 7 and 7:30 . if the pdf f(x)=k is used, what is k?

8) your state is administering COVID 19 test the CDC’s serologic test have a specificity of 99% (true negative) and 96% sensitivity (true positive) there are approcximately 170,000 cases of COVID 19 in new York with a population of 20 million. Your friend is randomly selected for a serologic test and it comes back positive. Given that your friend’s test is positive, what is the probability they actually have COVID 19

Answer #1

13)

Expected value of a single card

= 1/2*$0.50 + 3/10*$1 + 3/20*$5 + 1/20*$10

= $**1.80**

E(300X + 2) = 300*E(X) + 2 = $**542**

1)

k = **1/30**

8)

Let C denote the event of having COVID-19

and T denote the event of testing positive

P(C) = 170,000/20,000,000

= 0.0085

P(C') = 1 - P(C) = 0.9915

Specificity = P(T' | C') = 0.99

-> P(T | C') = 0.01

Sensitivity = P(T | C) = 0.96

P(T) = P(T | C)*P(C) + P(T | C')*P(C')

= 0.96*0.0085 + 0.01*0.9915

= 0.018075

The required probability = P(C | T)

= P(T | C)*P(C)/P(T)

= 0.96*0.0085/0.018075

= **0.45**

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