A crab catches a prey Once in every Three Days (1/3 is the probability to catch in One day). What will be the probability that it catches atleast one prey in 5 days.??
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Probability
Source: Beat The GMAT — Problem Solving |
one day in every three days turns success
1/3 is success rate and 2/3 is failure rate
at least one crab is caught in five days = one and more than one day's success
one day success -> 5C1 * 1/3 * (2/3)^4 +
two days success -> 5C2 * (1/3)^2 * (2/3)^3 +
three days success -> 5C3 * (1/3)^3 * (2/3)^2 +
four days success -> 5C4 * (1/3)^4 * (2/3)^1 +
five days success -> 5C5 * (1/3)^5 * (2/3)^0 =
OR take easy step to find complement probability, no crab is caught through five days (no success in five days) -> 1- 5C5 * (2/3)^5 = 1- 1*8/243 = 235/243
1/3 is success rate and 2/3 is failure rate
at least one crab is caught in five days = one and more than one day's success
one day success -> 5C1 * 1/3 * (2/3)^4 +
two days success -> 5C2 * (1/3)^2 * (2/3)^3 +
three days success -> 5C3 * (1/3)^3 * (2/3)^2 +
four days success -> 5C4 * (1/3)^4 * (2/3)^1 +
five days success -> 5C5 * (1/3)^5 * (2/3)^0 =
OR take easy step to find complement probability, no crab is caught through five days (no success in five days) -> 1- 5C5 * (2/3)^5 = 1- 1*8/243 = 235/243
john123 wrote:A crab catches a prey Once in every Three Days (1/3 is the probability to catch in One day). What will be the probability that it catches atleast one prey in 5 days.??
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