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The probability of having a head injury while bicycling from campus to my home without a...

The probability of having a head injury while bicycling from campus to my home without a helmet is 0.05, whereas the chances of having a head injury while bicycling with a helmet is much smaller at 0.01. Assuming I bike to campus every day for a month (with 30 days in the month), what is the probability that I keep my cranium intact for the whole month if I wear a helmet?

what is the probability that I keep my cranium intact for the whole month if I do not wear a helmet ?

Math   Statistics-And-Probability   
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Answer #1

The probability of having a head injury while bicycling from campus to my home without a helmet is 0.05.
So the the probability of not having a head injury while bicycling without a helmet = 1-0.05 = 0.95

The probability of having a head injury while bicycling with a helmet is 0.01

So the the probability of not having a head injury while bicycling with a helmet = 1-0.01 = 0.99


Each day of the month is independent to each other .
So the probability that I keep my cranium intact for the whole month if I wear a helmet = 0.99 * 0.99 * 0.99*.....0.99 (30 times) (Ans)

The probability that I keep my cranium intact for the whole month if I don't wear a helmet = 0.95 * 0.95 * 0.95*.....0.95 (30 times) (Ans)

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