There is a quiz show that is composed of three rounds. A contestant solves Question 1...

There is a quiz show that is composed of three rounds. A contestant solves Question 1 first and if she gets the right answer, then she will move on to next round to answer Question 2, and if she also answers correctly, then she will go to final round to answer Question 3. If she fails to answer correctly, then she is not allowed to go on to the next round. The probability that she knows the answer to Question 1 is 0.9, to Question 2 is 0.8 and to Question 3 is 0.7. What is the probability that she will win this quiz show?

(a) 0.504

(b) 0.56

(d) 0.72 15.

Given that she did not win this quiz show, what is the conditional probability that she failed to answer Question 2?

(a) 0.3571

(b) 0.3629

(d) 0.3839

Solutions

Expert Solution

probability that she knows the answer to Question 1 = 0.9

probability that she knows the answer to Question 2 = 0.8

probability that she knows the answer to Question 3 = 0.7

P[ She will win the quiz ] = P[ She will answer all correctly ] = 0.9*0.8*0.7

P[ She will win the quiz ] = 0.504

Given that she did not win this quiz show, what is the conditional probability that she failed to answer Question 2?

P[ She failed the quiz ] = P[ She fails at Question 1 ] + P[ She fails at Question 2 ] + P[ She fails at Question 3 ]

P[ She fails at Question 1 ] = 1 - 0.9 = 0.1

P[ She fails at Question 2 ] = 0.9*(1-0.8) = 0.9*0.2 = 0.18

P[ She fails at Question 3 ] = 0.9*0.8*(1-0.7) = 0.9*0.8*0.3 = 0.216

P[ She failed the quiz ] = 0.1 + 0.18 + 0.216 = 0.496

P[ She fails at Question 2 | she fails the quiz ] = P[ She fails at Question 2 ]/P[ She failed the quiz ]

P[ She fails at Question 2 | she fails the quiz ] = 0.18/0.496

P[ She fails at Question 2 | she fails the quiz ] = 0.3629

orchestra answered 1 year ago

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