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There is 30% chance that it rains on any particular day. The probability that there is at least one rainy day within a period of 7 days is

  • Option 1)

    1-(0.7)^{7}

     

     

     

  • Option 2)

    \frac{1-4(0.7)^{7}}{1-(0.7)^{7}}

  • Option 3)

    \frac{1-(0.7)^{7}}{1-4(0.7)^{7}}

  • Option 4)

      none of these

 

Answers (1)

best_answer

As we learned

 

Binomial Distribution -

In a series of n independent trials if the probability of success P in each trial is same, then the probapility of r success is

P(X=r)= \left\{\begin{matrix} \left ( \frac{n}{r} \right )\: q^{n-r}\cdot P^{r} & q = 1-P\\ \left ( \frac{n}{r} \right )\frac{1}{2^{n}} &P=\frac{1}{2} \end{matrix}\right.

- wherein

Where \sum is probability of failure.

 

 The probability of rainy day =p=\frac{3}{10}

 

The probability of a sunny day =q=1-\frac{3}{10}=\frac{7}{10}

Let E denote the event of at least one rainy day with in a period of 7 days.

Then P(E)=^{7}C_(1)q^{6}p+^{7}C_{2}q^{5}p^{2}+^{7}C_{3}q^{4}p^{3}+\cdots \cdots +^{7}C_{7}p^{7}

= (q+p)^{7}-^{7}C_{0}q^{7}=1-\left ( \frac{7}{10} \right )^{7}=1-(0.7)^{7}


Option 1)

1-(0.7)^{7}

 

 

 

Option 2)

\frac{1-4(0.7)^{7}}{1-(0.7)^{7}}

Option 3)

\frac{1-(0.7)^{7}}{1-4(0.7)^{7}}

Option 4)

  none of these

Posted by

Himanshu

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