Question

You’ve been hired as a consultant for a new planned NYC “quadrathalon”, in which participants run from Hunter’s Point South Park in Queens to Socrates Sculpture garden, take a kayak from there to Roosevelt Island,  swim from there to John Jay park on Manhattan, cycle across to the Boat Basin, then swim down to a concluding party at Riverside pier 1.  The organizers are worried about pollution while swimming in the two rivers.  Studies have show the East River has unacceptable pollution levels a percentage of time given by p_E in the data sheet, while the Hudson river has unacceptable levels p_Hof the time.  Assuming these probabilities are independent answer the following:

p_E =  52  p_H =  22   p_HE = 37

1. What is the probability of having only oneriver contaminated? (they can move the kayak section from one river to the other).
2. What is the probability of having neitherriver contaminated?

You have received new information: if the East River is contaminated, the chances of the Hudson river also being contaminated goes up to p_HE(Manhattan pollutes both).   Redo the questions above using this new information.

Answer 1

a) Probability of only one river contaminated = Prob(First river contaminated)*P(Second river not contaminated) + P(Second river contaminated)*P(First river not contaminated)

= (0.52*0.78) + (0.22*0.48)

= 0.4056 + 0.1056

= 0.5112 = 51.12% of time Answer

b) Probability of no river contaminated = Probability of first river not contaminated * Probability of second river not contaminated

= 0.48 * 0.78

= 0.3744 = 37.44% of time Answer

After new information:

a) Probability of only one river contaminated = Prob(East river contaminated)*P(Hudson river not contaminated) + P(Hudson river contaminated)*P(East river not contaminated)

= (0.52*0.63) + (0.22*0.48)

= 0.3276 + 0.1056

= 0.4332 = 43.32% of time Answer

b) Probability of no river contaminated = Probability of first river not contaminated * Probability of second river not contaminated

= 0.48 * 0.78

= 0.3744 = 37.44% of time Answer

NOTE: If you satisfy with this solution please give me a thumb up. Thank-you :)