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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 1292