Questions: You randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 9 (inclusively). What is the probability of selecting an 8 both times? The probability is . (Type an integer or a decimal. Do not round.)

You randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 9 (inclusively). What is the probability of selecting an 8 both times?

The probability is .
(Type an integer or a decimal. Do not round.)

Transcript text: You randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 9 (inclusively). What is the probability of selecting an 8 both times? The probability is $\square$ $\square$. (Type an integer or a decimal. Do not round.)

Solution

Solution Steps

Step 1: Determine the total number of possible outcomes for the first selection

The first integer is selected from 0 to 24, inclusively. This means there are $ 25 $ possible outcomes for the first selection.

Step 2: Determine the total number of possible outcomes for the second selection

The second integer is selected from 0 to 9, inclusively. This means there are $ 10 $ possible outcomes for the second selection.

Step 3: Calculate the probability of selecting an 8 in both selections

The probability of selecting an 8 in the first selection is $ \frac{1}{25} $. The probability of selecting an 8 in the second selection is $ \frac{1}{10} $. Since the selections are independent, the combined probability is: \[ \frac{1}{25} \times \frac{1}{10} = \frac{1}{250} \]

Final Answer

$\boxed{\frac{1}{250}}$

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