3. Given the following information summarizing a survey given to people on the b

Question

3. Given the following information summarizing a survey given to people on the beach asking them if they applied sunscreen today. You must phrase each problem in terms of the events: M (male), S (sunscreen) Apply sunscreenDid not apply Age Male Female 40 30 50 80 Find the probability that a randomly selected beachgoer applied sunscreen Phrase your problem using The Law of Total Probability. Find the probability that a randomly selected beachgoer is a male with sunscreen applied a. b. c. Find the probability that a randomly selected female applies sunscreen. d. Find the probability that if a beachgoer is seen using applying sunscreen it i:s a female. Are the choice application of sunscreen and gender dependent events? Explain your answer, using data from the table. e.

Explanation / Answer

from above data:

a)P(applied sunscream)=total number in sample who apply sunscream)/total sample size =90/200=0.45

b)

P(male and applied sunscream)=40/200=0.20

c)

P(female|applying sunscream)=P( emale and applying sunscream)/P(applying sunscream)=50/90=0.5556

d)

P(female)=130/200 =0.65 whcih is not equal to P(female|applying sunscream) ; therefore events application of sunscreen and gender are not independent.

hene they are dependent

apply did not apply total male 40 30 70 female 50 80 130 total 90 110 200

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