I just need someone to explain this question to me in detail please. My professo
ID: 3043857 • Letter: I
Question
I just need someone to explain this question to me in detail please. My professor gave the answer but I still don't understand how thye got to it. Thank you.
You have three jars filled with M & M’s. The first jar has 100 red, 100 blue, 100 orange, 100 yellow, and 100 green M & M’s. The second jar has 50 red, 50 blue, 50 orange, 50 yellow, 50 green, and 250 brown M & M’s. The third jar has 5 red and 495 brown M & M’s.
a) . If you pick one M & M from each jar, what is the probability that you will get one red, one blue, and one brown? 4 Answer: This problem is tricky because there are different ways to get the desired outcome. There are no browns in the first jar or blues in the third jar. You could pick: red from jar 1, blue from jar 2, brown from jar 3 (probability 495/25000) blue from jar 1, brown from jar 2, red from jar 3 (probability 1250/25000) blue from jar 1, red from jar 2, brown from jar 3 (probability 495/25000) Total probability = sum of all 3 = 2240/25000
Explanation / Answer
We have to pick one M & M' from each jar
We have to find probability that 1 red , one blue and 1 brown.
There are no browns in first jar and there are no blues in the third jar.
There are three possible cases to pick one red , 1 blue and 1 brown.
By multiplication principle
P ( To pick red from first jar, blue from second jar, brown from third jar) = (100*500) * ( 50 / 500) * (495/500)
= (1/5) *(1/10) *(495/500) = 495/25000
P(To pick red from second jar, blue from first jar, brown from third jar ) = (50/500)*(100/500)*(495/100)
= (1/10)*(1/5) * (495/500) = 495/25000
P( (To pick red from third jar, blue from first jar, brown from second jar ) = (5/500) * (100/500) * (250/500)
=(1/100)*(1/5) * (250/500)
=250/25000
By addition principle
P ( Getting one red , one blue and one brown) = (495/25000) +(495/25000) +(250 /25000)
= 1240/25000
= 0.0496
P ( Getting one red , one blue and one brown) =0.0496
jar No. Color Total Red Blue Orange Yellow Green Brown Jar No1 100 100 100 100 100 0 500 Jar No2 50 50 50 50 50 250 500 Jar No 3 5 0 0 0 0 495 500