The probability that a person has blue eyes is 16%. Three unrelated people are selected at random.
a. Find the probability that all three have blue eyes:
b. Find the probability that none of the three have blue eyes
c. Find the probability that one of the three has blue eyes
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
a. .16 * .16 * .16 = ?
b. .84 * .84 * .84 = ?
c. .16 * .84 * .84 = ?
I am so lost and I have test tomorrow. Thank you to anyone who can help
The probability that a person has blue eyes is 16%. Three unrelated people are selected at random.
a. Find the probability that all three have blue eyes:
b. Find the probability that none of the three have blue eyes
c. Find the probability that one of the three has blue eyes
stupid question...
A would be: 0.004096
B would be: 0.592704
C would be: 0.112896
Problem 6
The probability that a selected person has blue eyes is 1=3. What is the probability that in a group of
1000 people there are no more than 300 with blue eyes?
To answer these questions, we need to understand the basic concept of probability and how it applies to independent events. In this scenario, the eye color of each person is an independent event, meaning the probability of one person having blue eyes does not affect the probability of another person having blue eyes.
a. Find the probability that all three have blue eyes:
To find the probability that all three selected individuals have blue eyes, we need to multiply the individual probabilities of each event occurring. In this case, the probability of each person having blue eyes is 16%, or 0.16. Thus, we can calculate the probability of all three having blue eyes as:
P(all three have blue eyes) = P(first person has blue eyes) x P(second person has blue eyes) x P(third person has blue eyes)
= 0.16 x 0.16 x 0.16
= 0.00256
= 0.256%
Therefore, the probability that all three selected individuals have blue eyes is 0.256%.
b. Find the probability that none of the three have blue eyes:
To find the probability that none of the three selected individuals have blue eyes, we need to find the probability of each person not having blue eyes and multiply them together. The probability of each individual not having blue eyes is given by (1 - 0.16) = 0.84.
P(none have blue eyes) = P(first person does not have blue eyes) x P(second person does not have blue eyes) x P(third person does not have blue eyes)
= 0.84 x 0.84 x 0.84
= 0.592704
= 59.2704%
Hence, the probability that none of the three selected individuals have blue eyes is 59.2704%.
c. Find the probability that one of the three has blue eyes:
To find the probability that exactly one of the three selected individuals has blue eyes, we can envision three possible scenarios: the first person has blue eyes, the second person has blue eyes, or the third person has blue eyes. However, we need to subtract the cases where two or all three individuals have blue eyes because we only want the probability of exactly one person having blue eyes.
P(one has blue eyes) = [P(first person has blue eyes) x P(second person does not have blue eyes) x P(third person does not have blue eyes)]
+ [P(first person does not have blue eyes) x P(second person has blue eyes) x P(third person does not have blue eyes)]
+ [P(first person does not have blue eyes) x P(second person does not have blue eyes) x P(third person has blue eyes)]
P(one has blue eyes) = (0.16 x 0.84 x 0.84) + (0.84 x 0.16 x 0.84) + (0.84 x 0.84 x 0.16)
= 0.1152 + 0.1152 + 0.1152
= 0.3456
= 34.56%
Thus, the probability that exactly one of the three selected individuals has blue eyes is 34.56%.