Answer:
Probability of both digits being the same is a likely outcome (A) and;
The first digit is greater than the second digit is equally likely as the first digit less than the second digit (C)
Explanation:
Question:
Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *
a) probability of both digits being the same is a likely outcome
b) the probability that a number includes the digit 2 only once is 5/9
c) The first digit is greater than the second digit is equally likely as the first digit less than the second digit
d) 23 is an unlikely outcome
SOLUTION
Find attached how I got the value combination.
Forming a two-digit whole number with digit 1,2 and 3 where repetition is allowed:
11, 12, 13, 21, 22, 23, 31, 32, 33
Let's check which of the options are correct.
a) Is probability of both digits being the same is a likely outcome?
From the numbers we got: 11, 22 and 33 have both digits the same.
Yes, the probability is a likely outcome
Option A is correct
b) Let the probability that a number includes the digit 2 only once = Pr( 2 only once)
Pr( 2 only once) = (digits which have number 2 once / total number)
12, 21, 23, 32
Digits which have number 2 once = 4
Total = 9
Pr( 2 only once) = 4/9
4/9 is not same as 5/9
So option B is wrong
c)The first digit is greater than the second digit = 21, 31, 32 = 3 in total
the first digit less than the second digit = 12, 13, 23 = 3 in total
Yes, they are equal in number
Option C is correct
d) 23 is a likely outcome
Option D is wrong