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Find the indicated probability. a study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after graduation. find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating.

a. 2.550
b. 0.098
c. 0.035
d. 0.068

1 Answer

2 votes

Final answer:

The probability that 5 randomly selected graduates all find jobs in their chosen field within a year, given a 51% chance for each, can be found using the binomial probability formula and is approximately 0.035, corresponding to answer choice c.

Step-by-step explanation:

the indicated probability:

The probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating, given that each has a 51% chance of doing so, can be calculated using the binomial probability formula. The binomial probability formula is P(X) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, 'p' is the probability of success on a single trial, and '(1-p)' is the probability of failure, so we calculate this as:

P(5) = (5 choose 5) * (0.51)^5 * (1-0.51)^0

Since '5 choose 5' is 1 and any number raised to the power of 0 is 1, the formula simplifies to:

P(5) = 1 * (0.51)^5 * 1 = (0.51)^5

By calculating this, we get:

P(5) = 0.51^5 = 0.0349

Thus the probability that 5 randomly selected graduates all find jobs in their chosen field within a year is approximately 0.035, which corresponds to answer choice c.

User Swapnil Godambe
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