Name: Quiz #1 (Take-House) Math 3860 due at in class at 2pm on Tuesday, January

Question

Name: Quiz #1 (Take-House) Math 3860 due at in class at 2pm on Tuesday, January 30, (may also be handed in eartier at my office, Olney 428V) Read the problems carefully and show your work y fall on a triangular region. The region is divided into 3 congruent suberiangles as shown 1. What is the probability that the first raindrop lands in the shaded region? Hint: View a raindrop as a single poiat in the triangle What is the sample space? What is the eveni? How are evests to be measured 2. What is the probability that both raindrops land in the shaded region? 3. What is the probability that no raindrops land in the shaded region? 4. What is the probability that at least one raindrop lands in the shaded region? 5. What is the probability that exactly one raindrop lands in the shaded region?

Explanation / Answer

a)

Probablity of raindrop falls in shaded region = Area of shaded region/ Area of triangle = 1/3

b)

Probability that both raindrops falls in shaded region = 1/3*1/3 = 1/9

c)

Probablity that none falls in shaded region = (1-1/3)*(1-1/3) = 2/3*2/3 = 4/9

d)

Probabiity that at least one falls = 1- Probability that none falls = 1-4/9 = 5/9

e)

Probability that exactly one falls in the shaded region = 1/3*2/3 + 2/3*1/3 = 4/9

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