Question

1 Two events are mutually exclusive if they cannot occur at the same time.

True

False

2.

An apartment building has the following apartments:

	1 bedroom	2 bedroom	3 bedroom
1st floor	3	1	1
2nd floor	2	2	2
3rd floor	1	4	1

If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor?

		2/15
		2/7
		11/15
		15/17 3. What probability value would be needed to complete the following probability distribution? x -2 -1 0 1 2 P(x) 0.48 0.20 0.16 0.26 0.18 0.22 0.11 There is no value that would make this a probability distribution 4. Compute the probability of X successes.    n = 6, X = 4, p = 0.85 0.176 0.824 0.667 0.85 5 Find the mean for the values of n and p when the conditions for the binomial distribution are met.    n = 100, p = 0.4 24 40 4.9 60 6. According to an Internet posting, 80% of adults enjoy drinking beer. Choose a group of 4 adults at random. The probability that none of them enjoy drinking beer is: 0.250 3.200 0.200 0.410 7. Which is a probability distribution? X 1 2 3 4 5 P(X) 1/20 2/20 3/20 4/20 5/20 X 2 4 6 8 15 P(X) 1/19 3/19 4/19 4/19 7/19 X 1 2 3 4 5 P(X) 1/10 1/10 1/10 1/10 1/10 None of the above

Answer 1

1 Two events are mutually exclusive if they cannot occur at the same time.

True

2 If an apartment is selected at random,

Probability that it is not a 2 bedroom apartment on the 2nd floor = 1 - Probability that it is a 2 bedroom apartment on the 2nd floor

Probability that it is a 2 bedroom apartment on the 2nd floor = Number of 2 bedroom apartment on the 2nd floor / Total number of apartments

Total number of apartments = 3+1+1+2+2+2+1+4+1 = 17

Number of 2 bedroom apartment on the 2nd floor = 2

Probability that it is a 2 bedroom apartment on the 2nd floor = Number of 2 bedroom apartment on the 2nd floor / Total number of apartments = 2/17

Probability that it is not a 2 bedroom apartment on the 2nd floor = 1 - Probability that it is a 2 bedroom apartment on the 2nd floor = 1 - 2/17 = (17-2)/17 = 15/17

Ans 15/17

3

Given

x	-2	-1	0	1	2
P(x)	0.48	0.2	0.16	0.26	Z

Let the missing probability be 'Z'. For P(x) to be Probability Distribution,

Therefore,

0.48+0.2+0.16+0.26+Z =1

Z = 1 -(0.48+0.2+0.16+0.26) = 1-1 = 0

Ans :  There is no value that would make this a probability distribution

4 probability of X successes.

   n = 6, X = 4, p = 0.85

Binomial Distribution Proabability mass function

Substituting , n = 6, X = 4, p = 0.85 in the above, q =1 - p = 1 - 0.85 = 0.15

Ans : 0.176

5. mean for the values of n and p when the conditions for the binomial distribution are met.
   n = 100, p = 0.4

Mean of Binomail Distribution = np

Mean = 100 x 0.4 = 40

Ans 40