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QUESTION 8 8.1 A bag contains 3 blue marbles and 2 red marbles. A marble is taken from the bag, the colour is recorded and the marble is put aside. A second marble is taken from the bag, the colour is recorded and then put aside. 8.1.1 Draw a tree diagram to represent the information above. Show the probabilities associated with EACH branch, as well as the possible outcomes. (3) 8.1.2 Determine the probability of first taking a red marble and then taking a blue marble, in that order. (2) 8.2 A and B are two events. The probability that event A will occur is 0,4 and the probability that event B will occur is 0,3. The probability that either event A or event B will occur is 0,58. 8.2.1 Are events A and B mutually exclusive? Justify your answer with appropriate calculations. (3) 8.2.2 Are events A and B independent? Justify your answer with appropriate calculations. (3) [11]

          QUESTION 8
8.1 A bag contains 3 blue marbles and 2 red marbles. A marble is taken from the bag, the colour is recorded and the marble is put aside. A second marble is taken from the bag, the colour is recorded and then put aside.
8.1.1 Draw a tree diagram to represent the information above. Show the probabilities associated with EACH branch, as well as the possible outcomes. (3)
8.1.2 Determine the probability of first taking a red marble and then taking a blue marble, in that order. (2)
8.2 A and B are two events. The probability that event A will occur is 0,4 and the probability that event B will occur is 0,3. The probability that either event A or event B will occur is 0,58.
8.2.1 Are events A and B mutually exclusive? Justify your answer with appropriate calculations. (3)
8.2.2 Are events A and B independent? Justify your answer with appropriate calculations. (3)
[11]

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QUESTION 8
8.1 A bag contains 3 blue marbles and 2 red marbles. A marble is taken from the bag, the colour is recorded and the marble is put aside. A second marble is taken from the bag, the colour is recorded and then put aside.
8.1.1 Draw a tree diagram to represent the information above. Show the probabilities associated with EACH branch, as well as the possible outcomes. (3)
8.1.2 Determine the probability of first taking a red marble and then taking a blue marble, in that order. (2)
8.2 A and B are two events. The probability that event A will occur is 0,4 and the probability that event B will occur is 0,3. The probability that either event A or event B will occur is 0,58.
8.2.1 Are events A and B mutually exclusive? Justify your answer with appropriate calculations. (3)
8.2.2 Are events A and B independent? Justify your answer with appropriate calculations. (3)
[11]

Added by Carlos C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

07/27/2024

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00:01 In 8 .1, we have a bag containing three blue marbles and two red.

00:06 We take a marble, put the marble aside.

00:09 Take a second marble.

00:10 We want to start by drawing a three diagram here.

00:13 So we'll have the first choice.

00:15 It might be blue, it might be red.

00:17 Then we have the second choice.

00:19 Again, it might be blue, might be red.

00:22 Now, what's the probability? the first marble is blue.

00:26 Well, we have five marbles in the bag, three of them are blue, so that's a three out of five chance.

00:32 And a 2 out of 5 chance it is red.

00:35 Now let's pretend the first one is blue.

00:37 We take out of blue marble, put it to one side, go back in for a second.

00:41 What's the probability the second is blue? well, there are only 4 left and only 2 of them are blue.

00:47 So 0 .5 and 0 .5 for red.

00:51 If the first marble is red, well, there are 4 marbles left, 3 blue, 1 red.

00:57 So a 0 .75 and 0 .25 chance, respectively.

01:00 Three out of four and one out of four.

01:05 So there's the branches and at the end to combine the probabilities you multiply.

01:11 So 0 .6 times 0 .5 is the probability of blue, blue, 0 .3 for blue red, 0 .4 times 0 .75 is 0 .3 for red blue, and 0 .3, no, no, i wish, 0 .1 for red, red.

01:30 So those are the possible outcomes.

01:32 Notice they do add up to 1 or 100%, because we know one of these is going to happen.

01:38 What's for probability of getting a red followed by a blue in that order? well, that is red blue, that is 0 .3.

01:52 8 .2.

01:53 We have two events...

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