One concern that has been raised regarding vaccines for COVID-19 has been incidences of myocarditis (an inflammation of the heart muscle). In particular, researchers collected data from the Vaccine Adverse Event Reporting System (VAERS) and found that boys between the ages of 12 and 15 had a rate of 70.7 cases of myocarditis per million doses, or a probability of 70.7/1000000 = 0.000 0707.

During the Phase 3 trials for their vaccine for children ages 12-15, Pfizer performed a double blind study, with 1,121 individuals receiving the vaccine. If we suppose half of these were boys, this would mean a sample size of 561 boys ages 12-15.

Using these assumptions, what would be the probability of observing at least one case of myocarditis among the sample?

Round tothe nearestthousandth (i.e. 3 decimal places).