Compute the quantity requested in each problem. Give an exact answer if possible

Question

Compute the quantity requested in each problem. Give an exact answer if possible; otherwise, round to three places after the decimal. If you use a Geometric or Binomial distribution, say so and identify the parameter(s). If you use a CDF, mention how you computed it (chart or command).

2. Unlucky Albert decides to play roulette and bet on a single square until he wins. (There are 38 squares, each equally likely.)
(a) Find the probability that Albert will need to play not more than 40 rounds until he wins one.
(b) After losing thirty rounds in a row, he thinks to himself, “I’m surely due for a win soon! Let’s play just a few more.” Find the probability that Albert will need to play not more than 40 rounds until he wins one, given that he has lost (at least) 30 rounds already.

Explanation / Answer

here probability of win p=1/38

a) P(Albert will need to play not more than 40 rounds until he wins one)=P(X<=40)=1-P(he doe not win in first 40 games) =1-(37/38)40 =1-0.3441 =0.6559

b) probability that Albert will need to play not more than 40 rounds until he wins one, given that he has lost (at least) 30 rounds already =P(X<=40|X>30) =P(X<=10) =1-(37/38)10 =1-0.7659 =0.2341

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