Question

3. Marz-Or-Bust ™ Corp. has built a spaceship to send astronauts to colonize Mars. For safety, they install 3 mutually independent computer systems for controlling the mission. Each has an 80% chance of successfully completing the long journey, but as long as at least two of them are working, the ship will reach Mars. Determine the probability of a completed mission. SHOW work/reasoning for full credit.

Answer 1

Solution :

Let X be a random variable which represents that out of 3 computers, the number of computers that will work throughout the mission.

The probability that a computer will successfully complete the long journey = 0.80

Let's consider "a computer that will work throughout the mission" as success. So, we have only two mutually exclusive outcomes for each of the trials.

Probability of success (p) = 0.80

Number of trials (n) = 3

Since, probability of success remains constant for each of the trials, outcomes are independent and number of trials are finite, therefore we can consider that X follows binomial distribution with parameters n = 3 and p = 0.80.

The mission will be completed if at least two system will work throughout the mission. And we need to find the probability of a completed mission.

It means we need to find P(X = at least 2).

P(X = at least 2) = P(X = 2) + P(X = 3)

According to binomial probability law,

Where, p is probability of success.

Hence, the probability of a completed mission is 0.896.