Due to the sharp increase in the pressure of the domestic job market in China, the probability of finding a job with a bachelor's degree is now 0.4. If 20 people are known to have jobs, what is the probability that 8 of them have a bachelor's degree? (The result is accurate to 4 decimal places)
Question
Due to the sharp increase in the pressure of the domestic job market in China, the probability of finding a job with a bachelor's degree is now 0.4. If 20 people are known to have jobs, what is the probability that 8 of them have a bachelor's degree? (The result is accurate to 4 decimal places)
Solution
This is a binomial probability problem. The formula for binomial probability is:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success on a single trial
- n is the number of trials
- k is the number of successes
In this case:
- n = 20 (the number of people who have jobs)
- k = 8 (the number of people who have a bachelor's degree)
- p = 0.4 (the probability of a person having a bachelor's degree)
Substituting these values into the formula, we get:
P(X=8) = C(20, 8) * (0.4^8) * ((1-0.4)^(20-8))
Calculating the above expression gives a probability of approximately 0.2182 when rounded to four decimal places.
So, the probability that 8 out of 20 people who have jobs have a bachelor's degree is 0.2182.
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