Question

The number of years a Mars rover is expected to function on the surface of Mars is exponentially distributed with parameter λ = 0.25. If the company Budget Mars Explorer Inc. successfully lands a Mars rover on the planet Mars, what is the probability that it will be working for an additional 10 years after it last sent a communication to mission control?

Answer 1

the probability that it will be working for an additional 10 years after it last sent a communication to mission control is 0.0821

Explanation:

Given that;

years a Mars rover is expected to function on the surface of Mars λ = 0.25

probability that it will be working for an additional 10 years after it last sent a communication to mission control?

Now x is number of years a Mars rover function

f(x) = 0.25e^-0.25x , 0 < n < ∞

so

P( X>10 ) = ₁₀∫^∞ 0.25e^(-0.25n) dn

= e^(-0.25 × 10)

= e^(-2.5})

= 0.0821

therefore the probability that it will be working for an additional 10 years after it last sent a communication to mission control is 0.0821