Question

(b) Tired parents are trying to rest until morning, but Mollie, Alaina, and Carly tend to cry at random times, ensuring the parents will wake up, and sometimes be forced to stay up all night. On any given night, one and only one of these monsters will cry- there is a 10% chance Mollie will cry, a 50% chance Alaina will cry, and a 40% chance Carly will cry. There is a 30% chance that if Mollie cries, she will stay up all night; if Alaina cries. there is a 75% chance she will be up all night; if Carly cries, there is a 25% chance she will remain awake all night. i. Find the probability that either Alaina or Mollie kept the parents up all night. ii. If the parents were up the entire night, what is the probablity that Carly was the cause?

Answer 1

B Mollie = M = 0.1 Alaina = A=0.5, Carly = C=0.4 whole day = 0.3 whole night = 0.15 whole wight = 0.25 Moblie lept 6 P ( Alaina or Mollie kept parents up all night) = (605x0.75) + Co.4x0.78) the Alaina kept parents up all night - (0.5 x 0.75) + (0.180-3) = 0.405 Pl parents will be up) & (0.180.3) + Co.sx0.75) + (0.4x0.25) = 0.505 Pl Carly kept parents up) = 0.4x0.25 = 0.1 Ans Required = 0. 10.198