elliot wrote a computer program that randomly generates a number from 2 to 10. if he runs the program twice…

elliot wrote a computer program that randomly generates a number from 2 to 10. if he runs the program twice, what is the probability that the number generated both times is a prime number?\no 2/15\no 1/6\no 16/81\no 9/20

elliot wrote a computer program that randomly generates a number from 2 to 10. if he runs the program twice, what is the probability that the number generated both times is a prime number?\no 2/15\no 1/6\no 16/81\no 9/20

Answer

Explanation:

Step1: Count total numbers

The numbers from 2 to 10 are 9 numbers. So, when running the program once, there are 9 possible outcomes.

Step2: Identify prime numbers

The prime numbers from 2 to 10 are 2, 3, 5, 7. There are 4 prime numbers.

Step3: Calculate single - run probability

The probability of getting a prime number in one run of the program is $P_1=\frac{4}{9}$.

Step4: Calculate two - run probability

Since the two runs are independent events, the probability of getting a prime number both times is $P = P_1\times P_1=\frac{4}{9}\times\frac{4}{9}=\frac{16}{81}$.

Answer:

$\frac{16}{81}$