if 25% of U.S. federal prison inmates are not U.S. citizens, find the probility that two randomly selected federal prison inmates will not be U.S. citizens.
Not US .25
US .75
.25 x .25 = .0625
6.25%
To find the probability that two randomly selected federal prison inmates will not be U.S. citizens, we can use the concept of independent events.
Since the percentage of federal prison inmates who are not U.S. citizens is given as 25%, it means that 75% (100% - 25%) of the inmates are U.S. citizens.
To calculate the probability that the first selected inmate is not a U.S. citizen, we can use the fact that there is a 25% chance of selecting a non-U.S. citizen. This can be represented as P(A) = 0.25.
After the first inmate is selected, there will be one less inmate in the population, and the number of non-U.S. citizens will also decrease by one. Now, to calculate the probability that the second selected inmate is not a U.S. citizen, we can use the fact that 25% (0.25) of the remaining prisoners are non-U.S. citizens. This can be represented as P(B|A) = 0.25 because it is conditional on the first inmate not being a U.S. citizen.
To find the probability that both events (inmates) are non-U.S. citizens, we need to multiply the probabilities of each event occurring. This multiplication can be represented as P(A ∩ B) = P(A) * P(B|A).
Therefore, the probability that two randomly selected federal prison inmates will not be U.S. citizens is:
P(A ∩ B) = P(A) * P(B|A) = 0.25 * 0.25 = 0.0625
So, the probability that two randomly selected federal prison inmates will not be U.S. citizens is 0.0625 or 6.25%.