Math Destroyer Practice Test 1 #27

[Birddds]

Hello all, I have an inquiry on this question: "Half the population of Green Village is vegetarian, and 35% ride bicycles. If 20% are both vegetarian and ride bicycles, what is the probability that a person chosen at random from Green Village is either a vegetarian or rides a bicycle?". The solution is 50%-20%=30%, 35%-20%=15%, 30%+15%+20%=65%. I only vaguely understand why you would subtract 20% from 50% and 35%, but I'm having some trouble understanding why you would add it back in at the end. Thank you in advance for your time and responses!

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[byahnoob]

The answer is 65%.

50% vegetarian
35% ride bicycles
but you know that 20% are BOTH vegetarian and ride bicycles.

50%-20% = 30% are VEGETARIAN, but do not ride bicycles
35% - 20% = 15% ride BICYCLES, but are not vegetarian
20% are BOTH VEGETARIAN and ride BICYCLES

thus

30% + 15% + 20% = 65%

 

[Birddds]

I think i've just been misunderstanding what the question has been asking, thank you!

 

[csulapredental]

The answer is 65%.

50% vegetarian
35% ride bicycles
but you know that 20% are BOTH vegetarian and ride bicycles.

50%-20% = 30% are VEGETARIAN, but do not ride bicycles
35% - 20% = 15% ride BICYCLES, but are not vegetarian
20% are BOTH VEGETARIAN and ride BICYCLES

thus

30% + 15% + 20% = 65%

c


can you elaborate rather than re quote whats in the back of the book..

 

[SharkTooth_oohaha]

the easiest way I have found to do these is to make a venn diagram and write the percentages in the circles and work the math out from there.

so two overlapping circles: Vegetarian, and Bike riders. The overlapped portion would be bike riders that are also vegetarian.

I try to start with the given numbers that are absolutes. I.E. that 20% are bike riding vegetarians and thus, would belong in the overlapped portion. This number gives us the other percentages remaining. So, 50% of the population are vegetarian, minus 20% that are also bikers = 30% that are just vegetarians and not bikers. Similarly, 35% that are bikers minus 20% that are both = 15% that are just bikers and not vegetarians.

so the venn diagram would look like 30/20/15 (Veg/Both/Bikers) and the question asks the likelihood that a person is either a vegetarian or a biker... which all of those numbers would fall into. Thus you add them up and gives you 65%.

 

[csulapredental]

the easiest way I have found to do these is to make a venn diagram and write the percentages in the circles and work the math out from there.

so two overlapping circles: Vegetarian, and Bike riders. The overlapped portion would be bike riders that are also vegetarian.

I try to start with the given numbers that are absolutes. I.E. that 20% are bike riding vegetarians and thus, would belong in the overlapped portion. This number gives us the other percentages remaining. So, 50% of the population are vegetarian, minus 20% that are also bikers = 30% that are just vegetarians and not bikers. Similarly, 35% that are bikers minus 20% that are both = 15% that are just bikers and not vegetarians.

so the venn diagram would look like 30/20/15 (Veg/Both/Bikers) and the question asks the likelihood that a person is either a vegetarian or a biker... which all of those numbers would fall into. Thus you add them up and gives you 65%.

This made sense ily thanks!!!!