We have observed birds on airport runways and found on Saturdays, 6 birds arrive

Question

We have observed birds on airport runways and found on Saturdays, 6 birds arrive if there are no delays in landings during peak hours. Assume no delays for the next few questions. a) What is the probability, as you observe for an hour, that at least 6 birds arrive? b) What is the probability, as you observe for an hour, that less than 4 birds arrive? c) What is the probability, as you observe for an hour, that no less than 4 birds arrive? d) What is the probability, as you observe for an hour, that no more than 2 birds arrive? In a particular state's lottery, you pick 5 different numbers (white balls) between 1 and 47, and a another ball (red ball) between 1 and 25 for each $1 play. Once a ball is picked, it does NOT go back in the bin and the order does NOT matter. You MUST show your work for this question (Excel is OK). a) What is the probability of winning the big jackpot by picking all the numbers, both white and red balls? b) What is the probability of winning by picking all 5 white balls but not the red one? c) What is the probability of winning by picking 3 out of 5 white balls and the red one? d) What is the probability of only picking the red ball? e) How much is the expected return of winning the $2 prize in part c)? Use the following tree, to answer the next set of questions2: Find the probability that stock prices go up. b) Find the Probability economy grows and stock prices go up. c) Find probability that the economy grows given stock prices went up. d) Find the probability that stock prices went up given the economy grows. e) Find the probability that the economy slows given stock prices went up.

Explanation / Answer

6)

From the tree diagram we have folloiwng information:

P(G) = 0.70, P(S) = 0.30

P(U|G) = 0.80, P(D|G) = 0.20

P(U|S) = 0.30, P(D|S) = 0.70

(a)

By the law of total probability, the probability that stock prices go up is

P(U) = P(U|S)P(S) + P(U|G)P(G) = 0.30*0.30 + 0.80*0.70 = 0.09 0.56 = 0.65

(b)

The requried probability is

P(G and U) = P(U|G)P(G) = 0.80 * 0.70 = 0.56

(c)

P(G|U) = P(G and U) / P(U) = 0.56 / 0.65 = 0.8615

(d)

From the tree diagram we have

P(U|G) = 0.80

(e)

By the complement rule

P(S|U) = 1 - P(G|U) = 1 - 0.8615 = 0.1385

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