Question

The weather forecast says that there is a 20% chance of rain each of the 4...

The weather forecast says that there is a 20% chance of rain each of the 4 hours during which your picnic is scheduled. What is the probability that there will be no rain in 3 of the 4 hours?

Math   Statistics-And-Probability   
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Answer #1

The weather forecast says that there is a 20% chance of rain each of the 4 hours during which your picnic is scheduled. What is the probability that there will be no rain in 3 of the 4 hours?

Solution::

Let, define an event R that represent rain each of the 4 hours during which your picnic is scheduled.

So, P(R)=P(rain each hours)=20/100=1/5

P(R​​​​​​c)=P(no rain each hours)=1-1/5=4/5

We need to find,

What is the probability that there will be no rain in 3 of the 4 hours?

P(no rain in 3 of the 4 hours)

=P(1st,2nd,3rd hours no rain, 4th hours rain)+P(1st,2nd,4th hours no rain, 3rd hours rain)+P(1st,3rd,4th hours no rain, 2nd hours rain)+P(2nd,3rd,4th hours no rain, 1st hours rain)

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