candidate for public office has claimed that 60% of voters will vote for her. If 5 registered voters were sampled,
To calculate the probability that all 5 sampled voters will vote for the candidate, we can first consider that the candidate has claimed that 60% of voters will vote for her. This means that the probability of any randomly selected voter voting for her is 0.60 or 60%.
To find the probability of all 5 voters voting for her, we multiply the probability of each individual voter voting for her. Since the sampling is done without replacement (once a voter has been chosen, they cannot be chosen again), the probability will change with each selection.
Let's assume that the voters are chosen independently and randomly, and each voter's choice is independent of the others.
1) For the first voter:
The probability that the first voter will vote for the candidate is 60%, or 0.60.
2) For the second voter:
Since the first voter is not replaced, there are now only 4 voters left. The probability that the second voter will vote for the candidate is still 60%, so the probability is 0.60.
3) For the third voter:
Again, since the previous two voters are not replaced, there are now only 3 voters left. The probability that the third voter will vote for the candidate is still 60%, so the probability is 0.60.
4) For the fourth voter:
With 2 voters already selected and not replaced, there are now only 2 voters left. The probability that the fourth voter will vote for the candidate is 60%, so the probability is 0.60.
5) For the fifth voter:
With 4 voters already selected and not replaced, there is now only 1 voter left. The probability that the fifth voter will vote for the candidate is still 60%, so the probability is 0.60.
To find the probability that all 5 sampled voters will vote for the candidate, we need to multiply the individual probabilities together:
0.60 * 0.60 * 0.60 * 0.60 * 0.60 = 0.07776
So, the probability that all 5 sampled voters will vote for the candidate is approximately 0.07776, or 7.776%.