Question

What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have two letters followed by four numerals? (Round your answer to one decimal place.)

Answer 1

Answer:

Therefore, the probability is  P=0.5.

Step-by-step explanation:

We calculate the the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have two letters followed by four numerals.

We will calculate the required probability through complement. First, we find the probability that a license plate has all different the letters and all different the numbers.

We calculate the number of possible combinations:

$26^2\cdot 10^4=6760000$

We calculate  the number of favorable combinations:

$26\cdot 25\cdot 10\cdot 9 \cdot 8\cdot 7=3276000$

Therefore, the probability is

$P_1=\frac{3276000}{6760000}\\\\P_1=0.48$

Now, we get

$P=1-P_1\\\\P=1-0.48\\\\P=0.52$

Therefore, the probability is  P=0.5.