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

Question

Mathematics

Dahlia

3 May, 22:13

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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Trinity Delgado · Answer 1

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