SOLUTION: A boat charter of St. Lucia takes tourists on a daily dolphin/whale watch cruise. Its brochure claims an 81% chance of sighting a whale or a dolphin, and you can assume that sighti

Question 1047170: A boat charter of St. Lucia takes tourists on a daily dolphin/whale watch cruise. Its brochure claims an 81% chance of sighting a whale or a dolphin, and you can assume that sightings from day to day are independent.
(a) If you take the dolphin/whale watch cruise on two consecutive days, what is the probability that you see a whale or a dolphin on both days? (Enter your answer to four decimal places.)
(b) If you take the dolphin/whale watch cruise on two consecutive days, what is the probability that you see a dolphin or a whale on at least one day? (Hint: First compute the probability that this event does not occur. Enter your answer to four decimal places.)
(c) If you want to have a 97% probability of seeing a whale or a dolphin at least once, what is the minimum number of days that you will need to take the cruise? (Round your answer up to the next day.)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
See them both days is 0.81*0.81=0.6561
See them on at least one day is 1-not seeing them at all=1-(0.19^2)=0.9639
To have a 97% probability of seeing them at least once, then need less than or equal to 0.03 probability NOT to see them at all. 0.19^x=0.03
take logs of both sides
x log (0.19)=log (0.03)
x=log (0.03)/log(0.19)=2.11 days. That rounds up to 3 days, which would have been suspected from the answer to (b).
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