Question

The manager of a famous water park attraction states that:
• 70% of the visitors on a specific day ride the water slide
• of those visitors who ride the water slide, 35% also ride the bumper
boats on the same day.
(a) Let W denote the event that a visitor on that day rides the water slide,
and let B denote the event that a visitor on that day rides the bumper
boats. Write the information given in the two bullet points in symbolic
form.
(b) Calculate the probability that a randomly chosen visitor on that day
rides both the water slide and the bumper boats.
(c) Additional information is now given that 50% of the visitors on that day
ride the bumper boats. Calculate the probability that a randomly
chosen visitor who rides the bumper boats also rides the water slide on
the same day.
(d) What percentage of visitors on that day ride either the water slide or
the bumper boats, or both?
(e) For the park visitors on that day, are the events of riding the water slide
and riding the bumper boats independent? Give a reason for your
answer.

Answer 1

a) From the given information, we have P(W)=.70 and P(B|W)=.35

b) P(randomly chosen visitor rides both the water slide and the bumper boats)

=P( B and W)=P(W)*P(B|W)=.7*.35=0.245

c) P( randomly chosen visitor who rides the bumper boats also rides the water slide on the same day)

=P(W|B)=P(W and B)/P(B)=0.245/.50=0.49 (as P(B)=.50 is given).

d) P( riding either the water slide or the bumper boats, or both)=P(W or B)=P(W)+P(B)-P(W and B)=.70+.50-.245=0.955

Thus the required percentage is 95.5%

e) Since P(B|W)=.35 but P(B)=.50, we find P(B|W) is not equal to P(B). Thus B and W can not be independent.

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