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suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes. if we choose 5 members of the colony, what is the probability that at least one of them lives more than 87 minutes?

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The probability that at least one of them lives more than 87 minutes is 0.87.

Probability

In statistics, the possible way of happening a particular event is called probability.

Given,

Suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes.

Here we need to find if we choose 5 members of the colony, then what is the probability that at least one of them lives more than 87 minutes.

Here we know that,

Total number of members = 5

Life span = 87 minutes

Expected value = 100 minutes

So, the probability is calculated as,

=> 87 /100

=> 0.87

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