The Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%. The rest were brown. If you pick a THREE M&Ms in a row (assume with replacement), what is the probability that they are all Brown?
a. 0.09
b. 0.027
c. 0.3
d. 0.6

We have been given that the Masterfoods Company says that before the introduction of purple, yellow candies made up 20% of their plain candies, red another 20%, and orange, blue and green each made up 10%.

Probability of a yellow candy would be 0.20 and probability of a red candy would be 0.20.

Probability of orange candy would be 0.10, probability of blue candy would be 0.10 and probability of green candy would be 0.10.

The probability of brown candy would be [tex]1-0.20-0.20-0.10-0.10-0.10=0.30[/tex]

To find the probability that three candies are all Brown, we will use multiplication rule of independent events as:

[tex]0.30\times 0.30\times 0.30=0.027[/tex]

Therefore, the probability that that three candies are Brown would be 0.027 and option 'b' is the correct choice.

andromache andromache · Answer 2 · 2022-01-11T11:25:53+01:00

andromache andromache

11-01-2022

The probability that they are all Brown is option b. 0.027.

The calculation is as follows;

The probability of brown candy should be

= 1-0.20 -0.20 -0.10 - 0.10-0.10

= 0.30

Now

the probability should be

[tex]= 0.3^3[/tex]

= 0.027

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