Value of a probability

This assignment covers content from Unit 2 of the course. It assesses your knowledge of the concepts and rules that allow us to compute the probabilities related to events that occur when conditions are uncertain.

Instructions

Show all your work and justify all of your answers and conclusions, except for the True/False questions.

Keep your work to 4 decimals, unless otherwise stated.

(4 marks)

Circle True (T) or False (F) for each of the following statements:

T F {H, T} represents the sample space for an experiment of flipping two coins, each with heads (H) on one side and tails (T) on the other.

T F 13/12 represents a possible value of a probability.

T F Suppose that the probability of event A occurring is 1/5 and the probability of event B occurring is 3/7. If events A and B are mutually exclusive, the probability that A and B occur together is 0.

T F If a researcher samples without replacement, then future probabilities of the sampling process are unaffected by prior probabilities.

(7 total marks)

At a recent convention, a group of 60 doctors were classified according to their specialties. The number of doctors in each specialty was summarized as follows:

Pediatrician: 18 General Practitioner: 29 Surgeon: 4 Dermatologist: 9 If a doctor is selected at random, what is the probability that:

(1 mark)

the doctor is a dermatologist?

 

The probability is 0.15

 

(2 marks)

the doctor is either a pediatrician or a general practitioner?

The probability 0.84

 

 

 

(2 marks)

the doctor is not a pediatrician?

 

The probability is 0.3

 

 

(2 marks)

the doctor is neither a  ?

 

The probability is 0.36

 

(19 marks)

An analysis of blood donors examined blood type (A, B, AB or O) and whether the donor was male or female. The data is represented in the following table:

Gender   A B AB O
Male  (M) 35 16 2 40
Female  (F) 29 25 5 38

In the questions below, round all calculated probabilities to 4 decimal places.

(3 marks)

1. What is the probability that a randomly selected donor is female?

 

The probability 0.4

 

 

(4 marks)

1. What is the probability that a randomly selected donor is either male or has type O blood?

 

The probability is 0.43

 

 

 

(4 marks)

1. What is the probability that a randomly selected donor is neither female nor has type AB blood?

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