STA 301 – Applied Statistics
Spring 2008, Section B
Homework #4 
Key
Due Wednesday, February 13
Question 1
:
A candy dish contains a mixture of plain and peanut M&Ms of various colors.
We have
the following facts about the M&Ms in the dish:
•
80% are plain (no peanuts)
•
50% are brown
•
90% are either plain or brown (or both)
Suppose one M&M is selected from this dish at random.
(a)
What is the probability that it is a plain, brown M&M?
Rearranging the addition rule, we have:
P(plain
∩
brown) = P(plain) + P(brown) – P(plain
∪
brown)
= .8 + .5  .9 = .4
(b)
Suppose we are informed that the M&M drawn is brown.
What is the probability
that it is also plain?
P(plain  brown) = P(plain
∩
brown) / P(brown) = .4 / .5 = .8
(c)
Are the events “brown M&M drawn” and “plain M&M drawn” mutually
exclusive?
Why or why not?
Since P(plain
∩
brown)
≠
0, the two events are not
mutually exclusive.
(d)
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 Spring '08
 Noe
 Statistics, Probability, British B class submarine, The Dish, CHiPs

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