I already know the answers! Please give me an in depth explanation! Problem 22.)

Question

I already know the answers! Please give me an in depth explanation!

Problem 22.) In a gambling game, a player's final result is determined from the outcomes of three inde- pendent rounds of play. The probability of winning the first round of play is 0.65. The probability of winning the second round of play is 0.40. The probability of winning the third round of play is 0.20. Every player is given the opportunity to play all three rounds. What is the probability that a player wins at least one round of play? a. 0.052 b. 0.168 c. 0.948 d. 0.832 Problem 23.) Several houses in one neighborhood have been listed for sale in the month of May. A seasoned real estate broker believes the probability that her first listing will have a contract within 30 days is 0.75 and the probability that her second listing will have a contract within 30 days is 0.85. She further believes that the probability that at least one of these properties will have a contract within 30 days is 0.90 Assuming that these probabilities are correct, what is the probability that neither of these houses will go under contract within 30 days? a. 0.70 b. 0.05 c. 0.15 d. 0.10

Explanation / Answer

Answer:

P(winning 1st round)=0.65, thus P(losing 1st round)=1-0.65=0.35

P(winning 2nd round)=0.4, thus P(losing 2nd round)=1-0.4=0.6

P(winning 3rd round)=0.2, thus P(losing 3rd round)=1-0.2=0.8

P(player wins atleast 1 round)=1-P(player loses all 3)=1-(0.35)*(0.6)*(0.8)=0.832

Thus correct option is D

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