Suppose that during a recent 30-year period, there were eight volcanic eruptio
a2linetagadaW
Answered question
2021-09-22
Answer & Explanation
unett
Skilled2021-09-23Added 119 answers
Step 1
From provided information, during a recent 30-year period, there were eight volcanic eruptions sufficiently powerful to reduce the amount of power generated by solar panels by at least 20% for a period of a year i.e. \(\displaystyle{p}={0.20}\ {\quad\text{and}\quad}\ {n}={8}\).
The probability that during 25-year period, there will be two or more “Class D20 eruptions” can be calculated using binomial probability function.
The probability mass function is said to be binomial probability mass function if the probability mass function is given as:
\(\displaystyle{P}{\left({X}={x}\right)}=^{{{n}}}{C}_{{{x}}}{p}^{{{x}}}{\left({1}-{p}\right)}^{{{n}-{x}}}\)
Step 2
The probability that during 25-year period, there will be two or more “Class D20 eruptions” can be calculated as:
\(\displaystyle{P}{\left({X}\geq{2}\right)}={1}-{P}{\left({X}{<}{2}\right)}\)
\(\displaystyle={1}-{\left[{P}{\left({X}={0}\right)}+{P}{\left({X}={1}\right)}\right]}\)
\(\displaystyle={1}-{\left[^{\left\lbrace{8}\right\rbrace}{C}_{{{0}}}{\left({0.2}\right)}^{{{0}}}{\left({1}-{0.2}\right)}^{{{8}}}+^{{{8}}}{C}_{{{1}}}{\left({0.2}\right)}^{{{1}}}{\left({1}-{0.2}\right)}^{{{7}}}\right]}\)
\(\displaystyle={0.49668352}\)
So, probability that during 25-year period, there will be two or more “Class D20 eruptions” is \(\displaystyle{0.49668352}\approx{0.4969}\).
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