1 An urn has 7 balls that are identical except that 4 are white and 3 are red. A
ID: 3048692 • Letter: 1
Question
1 An urn has 7 balls that are identical except that 4 are white and 3 are red. A sample of 5 is selected randomly without replacement.
- What is the probability that exactly 3 are white and 2 are red?
- What is the probability that at least 3 of the balls are white?
2. Nap Lajoie has a lifetime batting average of 0.338. Assume that Nap Lajoie came to bat officially five times every game played. What would be Nap Lajoie's probability getting at least four hits in a game? (Round your answer to six decimal places.)
Explanation / Answer
#1.
5 balls from 7 can be selected in 7C5 ways
a)
Selecting 3 white from 4 can be done in 4C3 ways and 2 red from 3 can be done in 3C2 ways
Hence possible selections are 4C3 * 3C2 = 12
Required prob = 12/7C5 = 0.5714
b)
selecting 3 or 4 white balls can be done in 4C3*3C2 + 4C4*3C1 = 15
Required prob = 15/7C5 = 0.7143
#2.
P(X = k) = C(n,k) * p^k * q^(n-k)
n : number of trials (5)
k : number of successes (4 or 5)
p : probability of success (0.338)
q : probability of failure (1-p = 0.662)
P(X 4) = P(X = 4) + P(X = 5)
= C(5,4) * 0.338^4 * 0.662^1 + C(5,5) * 0.338^5 + 0.662^0
= 5 * 0.338^4 * 0.662 + 1 * 0.338^5
= 0.047613
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