Question

A bag contains 77 red marbles, 33 white marbles, and 10 yellow marbles. Let's call the event A "Drawing a red marble" and event B "Drawing a yellow marble". Are the events A and B mutually exclusive? Are the events A and B independent if the first marble is replaced before the second draw? Are the events A and B independent if the first marble is not replaced before the second draw? If one marble is drawn from the bag, what is the probability of drawing a yellow marble and a red marble (on the same draw)? If one marble is drawn from the bag and replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble? If one marble is drawn from the bag and not replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble?

          A bag contains 77 red marbles, 33 white marbles, and 10 yellow marbles. Let's call the event A "Drawing a red marble" and event B "Drawing a yellow marble". 
Are the events A and B mutually exclusive? 
Are the events A and B independent if the first marble is replaced before the second draw? 
Are the events A and B independent if the first marble is not replaced before the second draw? 
If one marble is drawn from the bag, what is the probability of drawing a yellow marble and a red marble (on the same draw)? 
If one marble is drawn from the bag and replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble? 
If one marble is drawn from the bag and not replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Rosina Dapaah

12/23/2021

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Step 1: Calculate the probability of drawing a yellow marble and a red marble on the same draw. Show more…

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A bag contains 77 red marbles, 33 white marbles, and 10 yellow marbles. Let's call the event A "Drawing a red marble" and event B "Drawing a yellow marble". Are the events A and B mutually exclusive? Are the events A and B independent if the first marble is replaced before the second draw? Are the events A and B independent if the first marble is not replaced before the second draw? If one marble is drawn from the bag, what is the probability of drawing a yellow marble and a red marble (on the same draw)? If one marble is drawn from the bag and replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble? If one marble is drawn from the bag and not replaced, then another marble is drawn, what is the probability of drawing a yellow marble then a red marble?

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00:03 So in this question, we are given red mables to be equal to 77, white mables to be equal to 33, and yellow mables to be equal to 1 ,010.

00:25 So this implies that the total mables will be equal to 77 plus 33 plus thousand and ten.

00:36 And this is equal to 1 ,120.

00:43 So now you know a is equal to drawing red marble.

00:49 So a is equal to drawing red marble.

00:57 You have b is equal to drawing yellow marble.

01:07 So for i, it says or one, the event's a and b mutually exclusive.

01:14 So we need to find the probability of a.

01:17 And this is equal to 77 over 1120 and this gives a 0 .06875.

01:30 Our probability of b is equal to one zero one zero over one two zero and this gives a 0 .9 -178.

01:46 So probability of a plus the probability of b will be equal to 0 .06875, plus 0 .90178 will be equal to 0 .973.

02:07 So the total probability is not equal to 1.

02:11 So therefore, a and b are not mutually exclusive event.

02:18 So the question two says, are the event, a and b independent.

02:26 If the first mobile is not replaced before the second draw.

02:35 So in no replacement, second draw is dependent on first draw, and therefore the probability of a and b changes.

02:45 So a and b are not independent...

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