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At a busy street intersection, it is estimated that a jaywalker will be hit by a car with probability $0.01$. Assuming the individual trips to be independent, find the probability that a jaywalker remains unhit if he crosses the street twice per day for $50$ days.

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    $\begingroup$ Please add your work and tell us where you have been stuck. $\endgroup$ – AvZ Mar 7 '15 at 18:44
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If the probability of being hit is $0.01$, this implies the probability of remaining un-hit is $1-0.01=0.99$ as both events are mutually exclusive.
Now, since the jaywalker crosses the road twice a day, the probability of being un-hit for a day is $$(0.99)^2$$ For $50$ days it simply is
$$((0.99)^2)^{50}=(0.99)^{100}\approx 0.366\ldots$$ Hope this clears up your problem.

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