A poll asked 500 adults if they thought Ontario should produce more, less or maintain current production of ethanol.
-160 people responded "more ethanol production"
-136 people responded "less ethanol production"
-155 people responded "maintain current production level"
-49 people had no opinion
Three people are selected at random from this sample
What is the probability that all 3 responded "less ethanol production"?
Seems to me just like drawing from a pack of cards without replacement.
p = 136/500 * 135/499 * 134/498 = 0.0198
Oh, probability! Probability is like trying to predict whether or not a clown will fit in a tiny car. It's all about the numbers, my friend. So, let's crunch some numbers for this little puzzle.
Out of the 500 adults in the poll, 136 responded "less ethanol production." Now, if we want to calculate the probability that all 3 people selected at random also responded "less ethanol production," we need to calculate the probability for each selection.
The first selection has a probability of 136/500, since there are 136 people out of 500 who responded "less ethanol production."
For the second selection, since the first person was not replaced, the probability becomes 135/499 (one less person who responded "less ethanol production," and one fewer person in total).
And finally, for the third selection, it becomes 134/498 (taking into account the two previous selections).
To find the probability of all three events happening, we multiply the probabilities together:
(136/500) * (135/499) * (134/498) ≈ 0.0645, or about 6.45%
So, the probability that all 3 people selected at random responded "less ethanol production" is approximately 6.45%.
And that's a clownishly fun way to tackle probability!
To calculate the probability, we need to find the probability of selecting one person who responded "less ethanol production" and then multiply that by the probability of selecting another person who responded "less ethanol production" and then multiply that by the probability of selecting a third person who responded "less ethanol production".
The probability of selecting a person who responded "less ethanol production" on the first draw is:
P(selecting "less ethanol production" on first draw) = (136/500)
Since we are selecting without replacement, the probability of selecting a person who responded "less ethanol production" on the second draw, given that the first person selected responded "less ethanol production," is:
P(selecting "less ethanol production" on second draw | first draw was "less ethanol production") = (135/499)
Again, since we are selecting without replacement, the probability of selecting a person who responded "less ethanol production" on the third draw, given that the first two people selected responded "less ethanol production," is:
P(selecting "less ethanol production" on third draw | first two draws were "less ethanol production") = (134/498)
To find the probability of all three people responding "less ethanol production," we multiply these probabilities together:
P(all 3 responded "less ethanol production") = (136/500) * (135/499) * (134/498)
Calculating this probability:
P(all 3 responded "less ethanol production") ≈ 0.0535 (rounded to four decimal places) or 5.35% (rounded to two decimal places)
Therefore, the probability that all three randomly selected people responded "less ethanol production" is approximately 0.0535 or 5.35%.
To find the probability that all three selected people responded "less ethanol production," we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since three people are selected at random from a sample of 500 adults, there are 500 possible choices for the first person, 499 possible choices for the second person, and 498 possible choices for the third person. Therefore, the total number of outcomes is calculated as follows:
Total number of outcomes = 500 * 499 * 498
Number of favorable outcomes:
Since 136 people responded "less ethanol production" out of the 500 adults, the number of favorable outcomes for each person being selected is as follows:
Number of favorable outcomes = 136 * 136 * 136
Now, we can calculate the probability using the formula:
Probability = Number of favorable outcomes / Total number of outcomes
Substituting the values, we have:
Probability = (136 * 136 * 136) / (500 * 499 * 498)
By evaluating this expression, we can find the probability that all three randomly selected people responded "less ethanol production."