Question

In the 2016 election, 30 states went to the republican candidate and 20 states went to the democratic candidate. of the 30 states that went republican, 29 were in the continental united states. of the 20 states that went democratic, 19 are in the continental united states. one state is selected at we select 4 states at random (with replacement) what is the probability that at least 1 of the states is in the continental u.s. and went republican?

a. 0.04
b. 0.96
c. 0.64
d. 0.36

Answer 1

The probability of selecting at least one continental U.S. state that voted Republican in four random picks (with replacement) is found by: 1 - (21/50)^4.

Step-by-step explanation:

The probability that at least one of the four randomly selected states is in the continental U.S. and went Republican can be found by subtracting the probability that none of the states selected fulfil that criterion from 1 (the total probability). Given that 29 out of 30 Republican states are in the continental U.S., the probability of selecting such a state is 29/50 (since there are 50 states in total).

To find the probability of not selecting a continental U.S. state that went Republican in any of the four picks (with replacement), we calculate (21/50)^4, as there are 21 states that either didn't go Republican or are not in the continental U.S. Hence, the complementary probability is 1 - (21/50)^4.