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29 November, 12:57

A somewhat disorganized hiker forgets to bring his insect repellant on 30% of his hikes. The probability of being bitten is 90% if he forgets the repellant and 20% if he uses the repellant. What is the probability that he will be bitten

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  1. 29 November, 14:07
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    41% probability that he will be bitten

    Step-by-step explanation:

    We have these following probabilities:

    A 30% probability that the hiker does not bring the repellant.

    A 100-30 = 70% probability that the hiker brings the repellant.

    If he brings the repellant, a 20% probability of being bitten.

    If he forgets the repellant, a 90% probability of being bitten.

    What is the probability that he will be bitten

    Two cases:

    Bitten with the repellant (20% of 70%)

    Bitten without the repellant (90% of 30%). So

    P = 0.2*0.7 + 0.9*0.3 = 0.41

    41% probability that he will be bitten
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