0
$\begingroup$

Earthquakes in another country Assume that in an other country the probability that during a year at least one earthquake happens is 0,3 . What is the probability that during 5 years the number of earthquakes is at least 3? Note: We need to apply "Poisson Distribution" for solving this problem.

Hi guys. I solved this problem with help of simple proportion. I said that if during 1 year probability is 0.3 , then during 5 is X and found X which is 1,5 . Thus probability is 1,5 . I just want to make sure that the result is right. Thanks in advance!

$\endgroup$
11
  • 2
    $\begingroup$ How could the probability be greater than $1$? $\endgroup$
    – lulu
    Commented Jan 2, 2019 at 21:12
  • $\begingroup$ It's certainly wrong. Probabilities must be between 0 and 1 $\endgroup$
    – Ray Bern
    Commented Jan 2, 2019 at 21:14
  • $\begingroup$ Note: as stated the problem really can't be solved. We don't even have enough information to compute the probability that there are at least $3$ earthquakes in a single year. $\endgroup$
    – lulu
    Commented Jan 2, 2019 at 21:16
  • $\begingroup$ @lulu that's right $\endgroup$
    – Murad Sh-ov
    Commented Jan 2, 2019 at 21:17
  • $\begingroup$ Hint: Let $X$ be the number of earthquakes that happen in 5 years. Then, $P\{X\geq 3\}=1-P\{X<3\}$. $\endgroup$
    – Ray Bern
    Commented Jan 2, 2019 at 21:18

1 Answer 1

Reset to default
1
$\begingroup$

If you want to use a Poisson distribution, the expected number in five years is $1.5$. That is the $\lambda$ parameter in the distribution, so the probability of $n$ earthquakes in $5$ years is $$P(n)=\frac {1.5^ne^{-1.5}}{n!}$$Now compute the probability of $0$ to $2$ earthquakes and subtract from $1$ to get the chance of at least $3$ earthquakes.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .