a computers random number generator produces random integers from 1 to 50. what is the probability that the…

a computers random number generator produces random integers from 1 to 50. what is the probability that the first 3 integers generated are single - digit numbers?\n0.0058\n0.0080\n0.5120\n0.5514

a computers random number generator produces random integers from 1 to 50. what is the probability that the first 3 integers generated are single - digit numbers?\n0.0058\n0.0080\n0.5120\n0.5514

Answer

Explanation:

Step1: Calculate single - digit numbers probability

The single - digit numbers from 1 to 50 are 1, 2, 3, 4, 5, 6, 7, 8, 9. So there are 9 single - digit numbers out of 50. The probability of generating a single - digit number in one trial is $p=\frac{9}{50}$.

Step2: Use multiplication rule for independent events

Since the generation of each number is an independent event, the probability that the first 3 integers generated are single - digit numbers is $P = (\frac{9}{50})^3$. [ \begin{align*} P&=\frac{9^3}{50^3}\ &=\frac{729}{125000}\ & = 0.005832\approx0.0058 \end{align*} ]

Answer:

0.0058