Question

5. For the given pair of events A and​ B, complete parts​ (a) and​ (b) below.

​A: A marble is randomly selected from a bag containing 10 marbles consisting of 1​ red, 6 ​blue, and 3

green marbles. The selected marble is one of the green marbles.

​B: A second marble is selected and it is the 1 red marble in the bag.

B.

b. The probability that events A and B both occur is____

​(Round to four decimal places as​ needed.)

7.The accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts​ (a) and​ (b) below. Are these events​ unlikely?

_ No_(Did_Not_Lie) Yes_(Lied)

Positive_test_result 9 22

Negative_test_result 40 15

a. Four of the test subjects are randomly selected with​ replacement, and they all had true negative test results.

b. Four of the test subjects are randomly selected without​ replacement, and they all had true negative test results.

a. The probability that all four test subjects had a true negative test result when they are randomly selected with replacement is

(Round to three decimal places as​ needed.)

Is such an event​ unlikely?

Yes, because the probability of the event is greater than 0.05

No, because the probability of the event is greater than 0.05

Yes, because the probability of the event is less than 0.05

No, because the probability of the event is less than 0.05

B. The probability that all four test subjects had a true negative test result when they are randomly selected without replacement is____

​(Round to three decimal places as​ needed.)

Is such an event​ unlikely?

Yes, because the probability of the event is greater than 0.05

No, because the probability of the event is greater than 0.05

Yes, because the probability of the event is less than 0.05

No, because the probability of the event is less than 0.05

Answer 1

Dear student, please post the quest one at a time.

5)The probability that events A and B both occur is  $P(A\cap B)=P(A)P(B\mid A)$

The probability that the marble is selected green marble =$P(A)=\frac{3}{10}=0.3$

The probability that the second marble is red marble given that the first marble is green( there is a total of 9 marbles and 1 red marble) =$P(B\mid A)=\frac{1}{9}$

b)The probability that events A and B both occur is =$P(A\cap B)=P(A)*P(B\mid A)=\frac{1}{9}*(0.3)=0.033$