Question

A study conducted at a certain college shows that 61​% of the​ school's graduates move to a different state after graduating. Find the probability that among 9 randomly selected​ graduates, at least one moves to a different state after graduating. Round to three decimal places as needed.

Answer 1

Probability that at least one moves to a different state after graduating is 0.999.

Explanation:

We are given that a study conducted at a certain college shows that 61​% of the​ school's graduates move to a different state after graduating.

Also, 9 graduates randomly selected​ and we have to find the probability that at least one moves to a different state after graduating.

The above situation can be represented through Binomial distribution;

`P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....`

where, n = number of trials (samples) taken = 9 graduates

r = number of success = at least one

p = probability of success which in our question is % of school's

graduates moving to a different state after graduating, i.e; 61%

LET X = Number of graduates moving to a different state after graduating

So, it means X ~
`Binom(n=9, p=0.61)`

Now, Probability that at least one moves to a different state after graduating is given by = P(X
`\geq` 1)

P(X
`\geq` 1) = 1 - P(X = 0)

=
`1-\binom{9}{0}* 0.61^(0) * (1-0.61)^(9-0)`

=
`1-(1 * 1 * 0.39^(9))`

=
`1-0.39^(9)` = 0.999

Therefore, Probability that among 9 randomly selected​ graduates, at least one moves to a different state after graduating is 0.999.

Answer 2

0.999 is the required probability

Explanation:

We are given the following information:

We treat graduates moving to a different state as a success.

P(graduates move to a different state) = 61% = 0.61

Then the number of adults follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 9

We have to evaluate:

`P(x\geq 1)\\=1 = P(x = 0)\\=1-\binom{9}{0}(0.61)^0(1-0.61)^9\\=1-0.0002\\=0.999`

0.999 is the probability that among 9 randomly selected​ graduates, at least one moves to a different state after graduating.