QUESTION 2 [15 Marks] (a) Suppose that 3 balls are randomly...

QUESTION 2 [15 Marks] (a) Suppose that 3 balls are randomly selected from a box containing 5 green and 4 white balls. Calculate the probability that both are green, (i) if the balls are drawn in succession, i.e. without replacement; and (ii) if the balls are drawn with replacement. (5) (5) (b) A laboratory test is 95% effective in detecting a certain disease when it is actually present. However, the test yields a false positive result in 1% of the health persons tested. Suppose that 0.05% of the total population have the disease. Calculate the probability that a person has the disease given that the test result is positive. (5)

Transcript

00:01 So we are given that we are having total 5 boxes.

00:10 Okay.

00:11 1, 2, 3, 4 and 5.

00:15 And each of the 5 boxes containing the 5 balls.

00:21 5 balls each containing the 5 balls.

00:26 And that five balls are having a red, a blue, a green, a purple and a yellow balls each of them.

00:44 So we just have to find out the probability of draw a ball at a random from each box with the probability data for the first the ball is yellow ball is yellow so let's get started to solution so for the first we want to find the probability that whatever the first ball we have drawn is nothing but an yellow so for yellow i am using y so this should be close to c every and each of the box are having only single yellow ball so possible outcomes will be 1 divided by the total number of balls in each is nothing but 5.

01:28 So total will be 5.

01:29 So it will be 1 by 5 that means equals to 0 .2.

01:32 So this will be the answer for first.

01:34 Now in similar way for the second we have to find the conditional probability that the second one is nothing but yellow with conditional probability to the first one is also yellow.

01:48 So this can be defined as the probability of the first as yellow with the second is also to be as yellow divided by the probability of the first as yellow.

02:06 We just applied the conditional probability formula here.

02:09 So as per the above we have seen that the probability for getting first as yellow is 1 by 5 multiply by second as yellow will again going to be 1 by 5 divided by the probability of getting a first as yellow is 1 by 5.

02:23 So 1 by 5 1 by 5 cancel 1 by 5 will come so that means 0 .2 again so this is the answer for second part now in the third part we have asked to find out the probability that all balls are same color whatever the balls you have drawn so all balls are of the the same color support that we have to use probability that all are red first...

Question

Please give Ace some feedback