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Lyme disease is a disease carried by ticks, which can be transmitted to humans by tick bites
Lyme disease is a disease carried by ticks, which can be transmitted to humans by tick bites. Suppose the probability of contracting the disease is 1 250 for each tick bite.
(a) What is the probability that you will not get the disease when bitten once? 249/250 Correct: Your answer is correct.
(b) What is the probability that you will not get the disease from your first tick bite and will get it from your second tick bite? (Assume the events are independent from one bite to the next.) ____________?
2. Suppose about 68% (0.68) of children in a particular country were living with both parents, 26.4% (0.264) were living with mother only, 3% (0.03) were living with father only, and 2.6% (0.026) were not living with either parent.
a. What is the expected value for the number of parents a randomly selected child was living with?__________
3. Suppose probability that a birth results in a boy is about 0.54. You offer a bet to an unsuspecting friend. Each day you will call the local hospital and find out how many boys and how many girls were born the previous day. For each girl, you will give your friend $1 and for each boy your friend will give you $1.
a) Suppose that on a given day there are three births. What is the probability (as a decimal) that you lose $3 on that day?_______________
What is the probability (as a decimal) that your friend loses $3? ______________
(b) Notice that your net profit is $1 if a boy is born and −$1 if a girl is born. What is the expected value of your profit for each birth (in $)? ___________
(c) Using your answer in part (b), how much can you expect to make after 1,000 births (in $)?
Expert Solution
1A. The probability that one will not get the disease would be
1-probability of getting the disease on bite
=1-1/250
=249/250
1B. THe probability of such an event
=probability of not getting the disease in the first bite*probability of getting the disease in second bite.
So,
249/250*1/250=249/62500
2. This expected value is
=probability if living with both parents*2+probability of living with mother*1+probability of living with father*1+probability of neither parents*0
=.68*2+.264*1+.03*1+.026*0
=1.654
3A. Losing 3 dollars means that all 3 births were girls. The probability of this is
=probability that first is a girl*probability that second is a girl*probability that third is a girl.
So,
probability of losing 3 dollars= .46*.46*.46
= 0.097336
Similarly,
probability of the friend losing 3 dollars= .54*.54*.54
= 0.157464
3B. The expected profit for us is= .54*1+.46*-1
= 0.08
3C. After 1000 births, we expect to make
=.08*1000=$80.
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