Question

A nearby star system has been found to have two habitable planets EGR2600a and EGR2600b. The probability of life being present on EGR2600a is 0.3 while the probability of life being present on EGR2600b is 0.4.

      (a) What is the probability of life being present on both planets if these events are independent?

      (b) What is the probability of life being present on at least one of the planets if these events are independent?

Answer 1

Let A be the event of life being present on EGR2600a
Let A be the event of life being present on EGR2600b
P(A) = 0.3
P(B) = 0.4
It can be proved for independent event that

P(ANB) = P(A)P(B)
l

P(ANB) = P(A)P(BC)


P(ANB) = P(A)P(B)


P(ANB) = P(A)P(BC)

• P(Life present on planet EGR2600a and life present on planet EGR2600b)
  
  = P(ANB) = P(A)P(B) = 0.3*0.4 = 0.12
  
• P(Life present on at least one planet)
  =1 - P(Life is not present in planet EGR2600a and life present on planet EGR2600b)
  
  Co-PLANB) = 1 = P(49)P(Bº) = 1 – (1 – 0.3) 4 (1 – 0,4) = 1- 0.7 * 0.6 = 1-0.24 = 0.76
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