Is this word problem worded incorrectly?

[ericbakuladavis]

[solved] Is this word problem worded incorrectly?

Here it is, verbatim:

You are performing an experiment to determine how well plants grow under different light sources. Out of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives either visible light or ultraviolet light?

I plugged the numbers into a formula and the answer matched the answer in the solution key. However, I am wondering if this is actually a feasible scenario...

If we add the numbers of plants (12 + 15 + 6), we get 33, not 30.

One could alternatively assume that the 6 plants that receive both types of light are counted among the visible light plants and among the UV plants. However, this would mean that there are 27 plants (12 + 15 with 6 of those falling into both categories).

Is there any way that there could actually be 30 plants?

Thanks for reading,

Eric

 

[Deleted member 4993]

Here it is, verbatim:

You are performing an experiment to determine how well plants grow under different light sources. Out of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives either visible light or ultraviolet light?

I plugged the numbers into a formula and the answer matched the answer in the solution key. However, I am wondering if this is actually a feasible scenario...

If we add the numbers of plants (12 + 15 + 6), we get 33, not 30.

One could alternatively assume that the 6 plants that receive both types of light are counted among the visible light plants and among the UV plants. However, this would mean that there are 27 plants (12 + 15 with 6 of those falling into both categories).

Is there any way that there could actually be 30 plants?

Thanks for reading,

Eric

What formula did you use - and what was the answer?

 

[JeffM]

Here it is, verbatim:

You are performing an experiment to determine how well plants grow under different light sources. Out of the 30 plants in the experiment, 12 receive visible light, 15 receive ultraviolet light, and 6 receive both visible and ultraviolet light. What is the probability that a plant in the experiment receives either visible light or ultraviolet light?

I plugged the numbers into a formula and the answer matched the answer in the solution key. However, I am wondering if this is actually a feasible scenario...

If we add the numbers of plants (12 + 15 + 6), we get 33, not 30. That assumption, as you yourself saw, cannot be correct.

One could alternatively assume that the 6 plants that receive both types of light are counted among the visible light plants and among the UV plants. However, this would mean that there are 27 plants (12 + 15 with 6 of those falling into both categories). Under that assumption, there are not 27 plants that received either one or two kinds of light because the 6 are included in the 12 and in the 15. When you add 12 and 15 you are counting the 6 twice. The proper way to add here is 12 + 15 - 6 = 21. Does the answer now make sense? If not read below.

Is there any way that there could actually be 30 plants?

Thanks for reading,

Eric

If I am understanding the thrust of your question, it does not involve probability theory or formulas. It involves counting the elements of overlapping sets and interpreting a deceptively worded problem. (I do not mind deceptively worded problems because in real life problems are not always presented clearly. Some might go as far as to say that problems in real life are almost never presented clearly.) But it is something of a trick question.

Number of plants that receive visible light, with or without ultraviolet light = 12
Number of plants that receive visible light and ultraviolet light = 6.
Number of plants that receive only visible light = 12 - 6 = 6.

Number of plants that receive ultraviolet light, with or without visible light = 15
Number of plants that receive visible light and ultraviolet light = 6.
Number of plants that receive only ultraviolet light = 15 - 6 = 9.

Number of plants that receive only visible light = 6.
Number of plants that receive only ultraviolet light = 9.
Number of plants that receive visible light and ultraviolet light = 6.

Number of plants that received visible light, ultraviolet light, or both = 6 + 9 + 6 = 21.

So what can we say with certainty about the 9 remaining plants?

 

[ericbakuladavis]

Subhotosh, [EDIT: 12:22 pm]

The formula I used was P(A or B) = P(A) + P(B) - P(A and B). So the probability that a randomly selected plant will have been exposed to either ultraviolet and visible light is equal to:

12/30 + 15/30 - 6/30 = 21/30 = 7/10

I knew to use this formula simply by following the "flow" of the book from which this problem came. It also matches up with Jeff's more thorough explanation.

Jeff,

Thank you for correcting my misunderstanding and explaining the problem. I now see that there are 9 plants which received neither visible nor ultraviolet light. That was the piece I was missing. So, yes, the question and the answer now make sense.