Question

you randomly select an integer from 0 to 24 (inclusively) and then randomly select an integer from 0 to 49 (inclusively). what is the probability of selecting a 3 both times? the probability is (type an integer or a decimal. do not round.)

Explanation:

Step1: Calculate the number of possible outcomes for the first selection

The integers from \(0\) to \(24\) (inclusive) give \(n_1=25\) possible outcomes.

Step2: Calculate the probability of selecting \(3\) in the first selection

Let \(P_1\) be the probability. Since there is \(1\) favorable outcome (selecting \(3\)), \(P_1=\frac{1}{25}\).

Step3: Calculate the number of possible outcomes for the second selection

The integers from \(0\) to \(49\) (inclusive) give \(n_2 = 50\) possible outcomes.

Step4: Calculate the probability of selecting \(3\) in the second selection

Let \(P_2\) be the probability. Since there is \(1\) favorable outcome (selecting \(3\)), \(P_2=\frac{1}{50}\).

Step5: Use the multiplication rule for independent events

Since the two selections are independent, the probability \(P\) of both events occurring is \(P = P_1\times P_2\). Substitute \(P_1=\frac{1}{25}\) and \(P_2=\frac{1}{50}\) into the formula: \(P=\frac{1}{25}\times\frac{1}{50}=\frac{1}{1250}= 0.0008\).

Answer:

\(0.0008\)