Chapter 5, Problem 5.60CE

It has been estimated that the odds of being struck by lightning in a given year are 1 to 240,000. Using this information: Source: lightningtalks.com. July 27, 2006.

a. Express the odds in terms of “odds against.”

b. What is the probability that a randomly selected individual will be struck by lightning this year?

c. What is the probability that the person in part (b) will be struck by lightning at least once during the next 20 years?

To determine

(a)

To express the odds in terms of "odds against"

Answer to Problem 5.60CE

"Odds against" is 240,000 : 1

Explanation of Solution

Given:

Odds of being struck by lightning in a given year = odds in favor= 1 : 240,000

Let, the odds against the occurrence of an event are the reverse of the odds in favor.

Therefore, odds against is 240,000 : 1

To determine

(b)

To find the probability that randomly selected individual will be struck by lightning the year.

Answer to Problem 5.60CE

The probability that randomly selected individual will be struck by lightning the year = $\frac{1}{240,001}$

Explanation of Solution

Given:

Odds of being struck by lightning in a given year = odds in favor = 1 : 240,000

Formula:

If the odds in favor of an event happening are A to B, or A:B, the probability being expressed is,

  $\frac{A}{A+B}$

Calculation:

In this case, A = 1 and B = 240,000

Therefore,

Probability that randomly selected individual will be struck by lightning the year

  $\frac{1}{240,000+1}=\frac{1}{240,001}$

To determine

(c)

To find the probability that the person in part b will be struck by lightning at least once during he next 20 years.

Answer to Problem 5.60CE

The probability that the person in part b will be struck by lightning at least once during he next 20 years= 0.0000834

Explanation of Solution

Given:

Probability that randomly selected individual will be struck by lightning the year

  = $\frac{1}{240,001}$

Calculation:

We already know the probability for a single year. So, to find probability for 20 years, we just need to multiply given probability by 20.

Therefore,

Probability that randomly selected individual will be struck by lightning the 20 years

  $\begin{array}{l}=20\times \frac{1}{240,001}\\ =0.0000834\end{array}$