SOLUTION: The probability that a fisherman catches a tuna in any one trip is 0.15 What is the probability, (3 decimals) that he catches a tuna on: At least one of three excursions? (The

Algebra ->  Probability-and-statistics -> SOLUTION: The probability that a fisherman catches a tuna in any one trip is 0.15 What is the probability, (3 decimals) that he catches a tuna on: At least one of three excursions? (The       Log On


   

Question 369672: The probability that a fisherman catches a tuna in any one trip is 0.15
What is the probability, (3 decimals) that he catches a tuna on:
At least one of three excursions? (The answer is .386, but how?)




Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at all of the possible outcomes for 3 excursions-C is catches, D is doesn't catch.
There are 2%5E3 possible outcomes.
CCC
CCD
CDC
CDD
DCC
DCD
DDC
DDD
Only one outcomes has him not catching at least one, DDD
P%28D%29=1-0.15=0.85
P%28DDD%29=%280.85%29%280.85%29%280.85%29=0.614125
P(DDD)+P(at least 1 C)=1
P(at least 1 C)=1-P%28DDD%29
P(at least 1 C)=1-0.614125
P(at least 1 C)=highlight%280.385875%29

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Note: The probability of x successes in n trials is: 

.

P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively. 

In this case p = .15 and q = .85

nCx = n%21%2F%28x%21%28n-x%21%29%29



P( at least one) = 1 - P(catching none) = 1 - (.85)^3 = 1 - .614 = .386