Question

. If p1, P2,... P., are the probabilities that certain events happen, than the probability that at least one of these events happens is
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Answer 1

Step-by-step explanation:

Let E

1

,E

2

,....E

n

be n independent events.

Given probabilities of these events as p

1

,p

2

,....p

n

Since, probability of happening of E

1

is p

1

Then probability of non-happening of event E

1

is 1−p

1

Similarly, probability of non-happening of event E

2

is 1−p

2

Similarly, probability of non-happening of event E

n

is 1−p

n

Now, probability of non-happening of any of the events is (1−p

1

)(1−p

2

)....(1−p

n

)

So, probability of happening of at least one event is 1−(1−p

1

)(1−p

2

)....(1−p

n

)