Question

If one of the 50 states is selected at random to be the site of a new nuclear power plant, find the probability that: (write your answer as a reduced fraction) SHOW YOUR WORK.

• The state begins with the letter A or the word North.
• The state borders Arkansas and begins with the letter T.

Answer 1

To find the probability, we need to determine the number of favorable outcomes (states that meet the given conditions) and the total number of possible outcomes (all 50 states).

1. The state begins with the letter A or the word North:

Favorable outcomes: Alaska, Alabama, Arizona, Arkansas

Total number of states: 50

2. The state borders Arkansas and begins with the letter T:

Favorable outcomes: Tennessee, Texas

Total number of states: 50

Now, we need to calculate the probability for each condition:

1. Probability of the state beginning with the letter A or the word North:

Number of favorable outcomes: 4

Probability = Number of favorable outcomes / Total number of states = 4 / 50 = 2 / 25

2. Probability of the state bordering Arkansas and beginning with the letter T:

Number of favorable outcomes: 2

Probability = Number of favorable outcomes / Total number of states = 2 / 50 = 1 / 25

Therefore, the probability that the selected state meets both conditions is the product of the individual probabilities:

Probability = (2 / 25) * (1 / 25) = 2 / 625

So, the probability that the selected state meets both conditions is 2/625.