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.