1. It has been determined that the probability of X occurring is equal to 0.06.
ID: 3042681 • Letter: 1
Question
1. It has been determined that the probability of X occurring is equal to 0.06. If Y and X are mutually exclusive and collectively exhaustive, what is the probability of Y?
2.
Responses to a mail survey are categorized along two dimensions -- A or B and X or Y. Thus, a given response could be AX, AY, BX or BY. A random sample of responses resulted in the following:
A
B
X
241
213
Y
140
466
What is the probability that a randomly selected survey will be a BY?
3. Responses to a mail survey are categorized along two dimensions -- A or B and X or Y. Thus, a given response could be AX, AY, BX or BY. A random sample of responses resulted in the following:
A
B
X
218
443
Y
366
265
What is the probability that a randomly selected survey will be an A OR X?
4.
A company operates two types of establishments -- Limited-Service and Full-Service -- in two regions -- J and K. This company's establishments are distributed as follows:
Region
Establishment Type
Limited-Service -
Full-Service
J
458
319
K
423
367
If we randomly selected a location in Region J, what is the probability that this location would be a Full-Service location?
5.
A company operates two types of establishments -- Limited-Service and Full-Service -- in two regions -- J and K. This company's establishments are distributed as follows:
Region
Establishment Type
Limited-Service
- Full-Service
J
323
441
K
423
465
If we randomly selected a Limited-Service location, what is the probability that this location would be in Region K?
A
B
X
241
213
Y
140
466
Explanation / Answer
1) Two mutually exclusive events are disjoint events and Collective exhaustive events cannot occur both at a time.
For a collective exhaustive event, the probability of total events= 1
If the probability X= 0.6 and Y= 1- X= 0.4
2) The probability that a randomly selected survey will be a BY:
Total number of events= 1060
Possible events of BY= 466
The probability of event occurring: 466/ 1060 =0.4396226
3)
The probability of A or X P(A or X): P(A) +P(X) -P( A and X)
The Event occurring of A and B= 218/1292
The event occurring of X= 661/ 1292
The event occurring of A= 584/ 1292
The probability of event occurring P(A or X) = 661/1292 + 584/1292 - 218/1292 =1027/ 1292 = 0.794892
A B Total X 218 443 661 Y 366 265 631 Total 584 708 1292Related Questions
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