Question

Bag A contains 3 green, 2 blue and 5 red balls and bag B contains 2 green, 3 red and 4 blue balls. A dice is rolled, if it gives a multiple of 3, bag A will be selected and 2 balls will be drawn. If the dice gives a multiple of 5, bag B will be selected and 2 balls will be drawn. If the dice gives neither a multiple of 5 nor a multiple of 3, one ball is drawn from each bag. What is the probability that both the balls are blue?

Answer 1

@kropot72

Answer 2

2/171

Answer 3

srry i couldnt able to delete the above one

Answer 4

my delete button is not working

Answer 5

What are the three values of probability for the three possible outcomes of rolling the dice?

Answer 6

2 blue balls from bag a and 4 blue balls in bag b so we should pick two

Answer 7

and also 2 balls will be drawn from bag a when it is a multiple of 3 and 2 balls from bag b will be drawn so multiple of 5

Answer 8

You need to answer my question to enable me to help you.
"What are the three values of probability for the three possible outcomes of rolling the dice?"
1. What is the probability of rolling a multiple of 3?
2. What is the probability of rolling a multiple of 5?
3 What is the probability of rolling neither a multiple of 5 nor a multiple of 3?

Answer 9

1)2/6 2)1/6 3)4/6

Answer 10

1/3,1/6,2/3

Answer 11

What is the probability of rolling neither a multiple of 5 nor a multiple of 3?
There are 3 outcomes that are neither a multiple of 5 nor a multiple of 3. They are 1,2 and 4.
So what is the correct value of probability?

Answer 12

1/2

Answer 13

oh srry i included 6 also

Answer 14

1/3*1/171+1/6*6/171

Answer 15

Consider the first case:
P(multiple of 3) = 1/3
If a multiple of 3 is rolled, what is the probability of drawing two blue balls from bag A?
There are initially 10 balls in bag A. The probability of drawing a blue ball on the first draw is 2/10. If a blue ball is drawn first, the probability of drawing a blue ball on the second draw is 1/9.
The probability of rolling a multiple of 3 and drawing 2 blue balls from bag A is given by:
\[\large \frac{1}{3}\times\frac{2}{10}\times\frac{1}{9}=\frac{2}{270}\]
Do you understand this step?

Answer 16

yes.1/135

Answer 17

from bag b means 1/6*4/9*3/8=12/432

Answer 18

1/36

Answer 19

so 4+15/540=19/540

Answer 20

You are correct for the second case!
Can you find the probability of the third case?

Answer 21

i think we dont need third case cuz if neither 5 or 3 so only one ball is drawn and not from a or b bag.we need two balls that to blue balls

Answer 22

19/540

Answer 23

Yes the third case is needed. Two balls are drawn, one ball from each bag A and bag B.

Answer 24

1/2*2/10*4/9

Answer 25

The probability of the third case is given by:
\[\large \frac{1}{2}\times\frac{2}{10}\times\frac{4}{9}=\frac{2}{45}\]
The three cases are mutually exclusive. Therefore the probability of 2 blue balls is:
\[\large P(2\ blue\ balls)=\frac{1}{135}+\frac{1}{36}+\frac{2}{45}=you\ can\ calculate\]

Answer 26

(20+75+120)/2700

Answer 27

215/2700

Answer 28

43/540

Answer 29

mutually exclusive means

Answer 30

\[\large \frac{1}{135}+\frac{1}{36}+\frac{2}{45}=\frac{4+15+24}{540}=\frac{43}{540}\]
You are correct!

Answer 31

Events are 'mutually exclusive' if it is impossible for them to happen together.
In your question the three cases must happen separately.