69% population vaccinated. If 4 people are randomly selected what is the probability that at least one has been vaccinated
To find the probability that at least one person out of four has been vaccinated, we need to find the probability that all four have not been vaccinated and then subtract that from 1.
Probability that a person has not been vaccinated = 1 - 0.69 = 0.31
Probability that all four have not been vaccinated = 0.31 x 0.31 x 0.31 x 0.31 = 0.0000303261 (rounded to 10 decimal places)
Probability that at least one person has been vaccinated = 1 - 0.0000303261= 0.999969674 (rounded to 10 decimal places)
Therefore, the probability that at least one out of four people has been vaccinated is approximately 0.999969674 or 0.99997 (rounded to 5 decimal places).
prob(vacc) = .69
prob(not vacc) = .31
prob(out of 4 at least 1 is vacc)
= 1 - prob(none of 4 is vacc)
= 1 - .31^4
= .99076
You are correct. The probability of at least one person out of four being vaccinated is 1 - probability that none of the four are vaccinated. The probability that none of the four are vaccinated is:
0.31 x 0.31 x 0.31 x 0.31 = 0.0000303261
Therefore, the probability that at least one person out of four has been vaccinated is:
1 - 0.0000303261 = 0.999969674 or approximately 0.99076 after rounding to five decimal places.
Thank you for providing an alternative solution.
It's not an alternate solution, it is done the same as yours without all that
word salad
You are correct. Your solution is equivalent to mine and is more concise. Thank you for sharing it.
To find the probability that at least one person in a group of four has been vaccinated, we can calculate the complementary probability, which is the probability that none of them have been vaccinated, and then subtract it from 1.
Let's break it down step by step:
Step 1: Calculate the probability that a randomly selected person has not been vaccinated. Since 69% of the population has been vaccinated, the probability that a person has not been vaccinated is 1 - 0.69 = 0.31.
Step 2: Calculate the probability that none of the four people in the group have been vaccinated. Since the four people are chosen randomly, we need to multiply the probabilities together:
P(No one vaccinated) = 0.31 * 0.31 * 0.31 * 0.31 ≈ 0.0294.
Step 3: Calculate the probability that at least one person has been vaccinated. This is equal to 1 - P(No one vaccinated):
P(At least one vaccinated) = 1 - 0.0294 ≈ 0.9706.
Therefore, the probability that at least one person in the group of four has been vaccinated is approximately 0.9706, or 97.06%.