Question

probability of a 10 year flood occurring at least once in the next 5 years is​

Answer 1

Answer:

1/2 mark me brainliest

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO DETERMINE

The probability of a 10 year flood occurring at least once in the next 5 years

FORMULA TO BE IMPLEMENTED

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

CALCULATION

By the given condition

$\displaystyle \sf{ p = \frac{1}{10} \: \: \: and \: \: \: n = 5} \: \:$

So

$\displaystyle \sf{ q=1 - \frac{1}{10} = \frac{9}{10} } \: \:$

Hence the probability of flood occurring at least once in the next 5 years

$\sf{ = P(X \geqslant 1)}$

$\sf{ =1 - P(X < 1)}$

$\sf{ =1 - P(X = 0)}$

$\displaystyle \sf{ = 1 - \large{ {}^{5} C_0}\: { \bigg( \frac{1}{10} \bigg)}^{0} \: \bigg( \frac{9}{10} \bigg)}^{5 - 0}\: \: \: \:$

$\displaystyle \sf{ = 1 - \bigg( \frac{9}{10} \bigg)}^{5 }\: \: \: \:$

$\displaystyle \sf{ = 1 - 0.59 }$

$\displaystyle \sf{ = 0.41 }$

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