Question

a message of length 5 digits is to be sent. each digit can be a 0, 1, or 2. if every message is equally likely, what is the probability that the message consists of 2 zeros, 2 ones, and 1 two? round your answer to have four decimal places.

Answer 1

The probability of a 5 digit message having 2 zeros, 2 ones, and 1 two, we divide the number of such arrangements (10) by the total number of messages possible (3^5 or 243), which gives a probability of approximately 0.0412.

Step-by-step explanation:

The question is asking to calculate the probability of receiving a message that consists of exactly 2 zeros, 2 ones, and 1 two. Given each digit in the message can be 0, 1, or 2, there are 3 possibilities for each digit in the message. Since the message is of length 5 digits, the total number of possible messages is 35, which is 243.

To find the number of messages that have 2 zeros, 2 ones, and 1 two, we need to use the formula for combinations. For this message configuration, the number of ways you can arrange 2 zeros, 2 ones, and 1 two is given by 10 (which is the result of 5! / (2!2!1!)).

Therefore, the probability of the message being 2 zeros, 2 ones, and 1 two is obtained by dividing the number of favorable outcomes (10) by the total number of possible messages (243), which gives us approximately 0.0412 when rounded to four decimal places.