# Ten students begin college at the same time. The probability of graduating in four years is 63%. Which expanded expression shows the first and last terms of the expression used to find the probability that at least six will graduate in four years?

The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term:

Last term:

To find the probability that at least six students will graduate in four years, we can use the binomial probability formula.

The first and last terms of the expanded expression for this probability can be determined using the binomial coefficients.

The binomial probability formula is given by:

Where:

P(X ≥ k) is the probability that X is greater than or equal to k,

n is the number of trials (students in this case),

k is the desired number of successes (six or more students graduating),

p is the probability of success in a single trial (probability of graduating in four years).

In this case, the number of trials (n) is 10, and the probability of success (p) is 0.63.

To find the first term, we substitute k = 6 into the formula:

C(10, 6) represents the binomial coefficient, which can be calculated as:

C(10, 6) = 10! / (6! * (10 - 6)!)

To find the last term, we substitute k = 10 into the formula:

C(10, 10) = 10! / (10! * (10 - 10)!)

Hence, The first and last terms of the expanded expression for the probability that at least six students will graduate in four years are:

First term:

Last term:

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Answer: Since this is dealing with binomial you do something like this

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