QuestionWhat is the probability that at least one of four randomly selected people has been vaccinated if are vaccinated? Round to three decimal places.
Studdy Solution
STEP 1
Assumptions1. The population is large enough that the probability of selecting a vaccinated person remains constant at66% for each selection.
. The selections are independent, meaning the outcome of one selection does not affect the outcome of another.
3. We are looking for the probability that at least one person is vaccinated, which includes the possibilities of one, two, three, or all four people being vaccinated.
STEP 2
The probability of at least one event happening is equal to one minus the probability of that event not happening at all. In this case, the event is "a person being vaccinated". So, we need to find the probability of none of the four people being vaccinated and subtract it from1.
STEP 3
The probability of a person not being vaccinated is the complement of the probability of a person being vaccinated. So, we subtract the given probability of vaccination from1.
STEP 4
Plug in the given value for the probability of vaccination to calculate the probability of not being vaccinated.
STEP 5
Calculate the probability of a person not being vaccinated.
STEP 6
The probability of none of the four people being vaccinated is the product of the probability of each person not being vaccinated, since the selections are independent.
STEP 7
Plug in the value for the probability of not being vaccinated to calculate the probability of none of the four people being vaccinated.
STEP 8
Calculate the probability of none of the four people being vaccinated.
STEP 9
Now, plug in the value for the probability of none of the four people being vaccinated into the equation for the probability of at least one person being vaccinated.
STEP 10
Calculate the probability of at least one person being vaccinated.
The probability that at least one of the four people selected has been vaccinated is0.987, rounded to three decimal places.
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