7.6.2: Risk of Death from a Shark Attack
- Page ID
- 64116
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The Florida Museum devotes an entire section of their website (www.floridamuseum.ufl.edu) to the lifetime risk of fatality due to shark attack with comparisons to other types of accidental death. The purpose of the research is to emphasize the point that even though sharks have a deadly and dangerous reputation, the actual chance of becoming a victim of a shark fatality is rather low compared with many other activities that we may participate in regularly.
The website states that the odds of suffering a shark-related fatality within your lifetime is 1 in 4,332,817. This compares to 1 in 5 odds for dying from heart disease, 1 in 7 odds for dying from cancer, 1 in 84 odds for having a fatal car accident, and 1 in 79,746 for dying from lightning. The odds of a fatal shark stack are clearly much smaller than any of these other common causes of fatalities. We will compare these odds more directly by first converting them to probabilities and then by calculating the odds ratios of a shark fatality compared to these other types of fatalities.
We will first convert these odds to probabilities. The odds of dying from heart disease is 1 in 5 so that the probability of dying from heart disease during your lifetime is \(1/(5+1)=1/6\approx 0.1667\). Similarly, the probabilities for dying from cancer is \(1/8=0.1250\), having a fatal car accident is \(1/85≈0.0118\), and dying from a lightning strike is \(1/79747≈0.0000125\). Converting the odds of dying from a shark attack yields a probability of \(1/4332818≈0.000000231\). Clearly we can observe that the probability suffering a fatal shark attack is much less than each of these outcomes.
Now let us compute the odds ratio comparing a shark attack to a couple of the other outcomes. We first compare the odds of dying from heart disease against the odds of dying from a shark attack. The odds of dying from heart disease are reported as 1 in 5 so that \(m=1\) and \(n-m=5\). The odds of dying from a shark attack are 1 in 4,3323,817 so that \(k=1\) and \(l-k=4332817\). Therefore, the odds ratio is
\[ \text{odds ratio} = \frac{m(l-k)}{k(n-m)} = \frac{1\times 4332817}{1\times 5} = \frac{4332817}{5} \approx 866563.4, \nonumber \]
which shows of course that the odds of dying from heart disease are much greater than the odds of dying from a shark attack. The closest risk we can find in the data is when we compare the odds of dying from a lightning strike compared against the odds of dying from a shark attack. The odds of dying from a lightning strike are reported as 1 in 79746 so that \(m=1\) and \(n-m=79746\) . Therefore, the odds ratio is
\[ \text{odds ratio} = \frac{m(l-k)}{k(n-m)} = \frac{1\times 4332817}{1\times 79746} = \frac{4332817}{79746} \approx 54.33, \nonumber \]
which shows that the odds of dying from a lightning strike are about 54 times the odds of dying from a shark attack.
The purpose of the information on the website is to alleviate fears about shark attacks on the Florida coast. As with any study of this type, one needs to interpret the odds and the probabilities in context. To compute the odds, the number of deaths of each type was compared to the population of the United States in 2021. The risk was averaged over about 70 years, the current life expectancy of the population. First and foremost, these odds then apply to individuals who live in the United States. Furthermore, this is a risk that aggregated over the entire population and may not apply singly to each individual person. For example, a person who practices a healthy lifestyle may have much lower odds of dying from a heart attack. Individuals who do not use tobacco products are likely to have much lower odds for cancer. The odds of dying in a fatal car accident may depend on where one lives and drives, and if they drive at all. Finally, one can lower the odds of being the victim of a fatal shark attack by simply not going in the ocean. Hence, while these odds make for interesting comparisons, it is much more accurate to simply report the number of fatalities of each type, noting that relatively few people die from shark attacks each year.