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August 14th, 2017, 08:15 AM   #1
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Probability query - baseballs, softballs and tennis balls

Hi All,

Wondering if anyone can lend a hand. I don't think I particularly have a problem with maths, but I am doing an online module, and my lecturers don't always provide the best answers.

I got a question wrong in an assignment, (multiple choice), and queried it, and I have convinced myself that I am right... Am I wrong? What am I missing? Below is the message to and from my lecturer


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Author Message
R J PRINSLOO
Good day

I have a query regarding assignment 6, question 8. Question 8 states:

A box contains 3 baseballs, 7 softballs and 11 tennis balls. Suppose P (baseball) denotes the probability of randomly selecting a baseball from the box. Which of the following statements is/are true?

A. The probability that a ball selected at random will not be a tennis ball is 1 − P (tennis ball) = 1 – 11/21 = 10/21 .

B. The probability that a ball selected at random will be a baseball or a softball is 3/21 × 7/21 = 1/21.

C. Suppose one tennis ball is taken out, and another ball is then randomly selected. The probability that it will be a softball is 7/20.

1. Only A

2. Only B

3. Only C

4. Only A and C

5. A, B and C


The lecturers answer was 5, A, B and C. However that is wrong. B is false. If we select one ball at random, the probability will be 10/21 that it will be either one of the balls described.


Another logic behind this, if my probability of getting a softball is 7/21, and the probability of getting a baseball is 3/21, how can the probability of the event be getting smaller, when the event (softball or baseball) is getting bigger? If I list the sample space, I have 21 events. From those 21 events, 3 are baseballs, 7 are softballs, leaving me with 10 events, of a total of 21 events that meet the criteria.


If the question stated that I draw 2 balls, what is the probability that one is a baseball, and one is a softball, then we can multiply, but even then, it will be 3/21 * 7/20, seeing that with our second selection, there is now only 20 balls left, seeing that one was drawn in our first selection. And even this calculation does not equal 1/21.


So the answer has to be 4, A and C is true.


Am I missing something perhaps?

(2017-08-13 15:09:21)
R J PRINSLOO
Hi Mr ********,


I am well aware that it didn't say two and only one.

The probability that it is a baseball is 3/21.

The probability that it is a softball is 7/21.

How can the probability that it is a baseball or softball decrease?

Below is the sample space of all possible 21 events, the ones in bold, represent baseball or softball. if I count them, it is 10, out of a total of 21 possibilities:

{baseball, baseball, baseball, softball, softball, softball, softball, softball, softball, softball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball, tennisball}

Hence, if I count all the baseballs, and softballs, it is 10/21, if I select one ball at random, from my sample space.

How can B be true?

(2017-08-14 16:56:11) Click to delete the message
Mr *******

The question says "a (ONE) ball selected at random". It didn't say TWO balls selected at sequence.
In that sense, If a ball is selected at random, The probability that it'll be a baseball or a softball is 3/21 × 7/21 ==> 21/441 ==> 1/21

The case for your argument is definitely wrong and the statement B is definitely TRUE.

Last edited by skipjack; August 27th, 2017 at 04:50 AM.
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August 26th, 2017, 09:32 PM   #2
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Sorry about the delay.
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August 26th, 2017, 09:37 PM   #3
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It should be
4. Only A and C
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August 27th, 2017, 04:38 AM   #4
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The lecturer seems to have gone out of his way to use "unexpected" interpretations.

In (B), one could interpret "a baseball or a softball" as meaning "one particular ball (that happens to be a baseball or a softball)", and that would explain the lecturer's reply. However, I would regard that interpretation as unreasonable, given the wording used in the problem.

In general, problems of this type can be difficult to state unambiguously, allowing a variety of answers, depending on what assumptions are made. In this instance, however, just begin your answers with an assertion such as "I believe the question's best (and intended) interpretation implies the following assumptions should be made:" and then state carefully the assumptions that you will use, ensuring that they justify your calculation(s). If the question is being marked electronically and such a preamble can't be entered, you can still explain your assumptions in a further polite communication to the lecturer.
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