Ross forms all two-digit whole numbers using digits 1, 2, and 3. He allows digits to repeat. Select statement(s) that are CORRECT. *

probability of both digits being the same is a likely outcome
the probability that a number includes the digit 2 only once is 5/9
first digit greater than the second digit is equally likely as the first digit less than the second digit
23 is an unlikely outcome

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)

Step-by-step 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

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.