Question

The probability that a grade 12 student has completed their 40 hours of community service is 5/6. The odds of a grade 12 student taking data management is 4/11.

a) Find the probability that a grade 12 student has completed their 40 hours of community service and is taking data management.

b) Find the probability that a grade 12 student is in data management, but has yet to hand in their community service hours.

c) Find the probability that a grade 12 student is taking data management or has handed in their community service hours.

Clearly label each part and show your work.

Answer 1

(a) Both the events are independent, hence probability that a grade 12 student has completed their 40 hours of community service and is taking data management = (5/6)*(4/11) = (10/33)

(b) probability that a grade 12 student is in data management, but has yet to hand in their community service hours is given by P(Data management)*P(has not completed 40 hours of community service)
= (4/11)*(1 - 5/6) = (4/11)*(1/6) = 2/33

(c) Probability that a grade 12 student is taking data management or has handed in their community service hours is
P(data management) + P(community service) - P(data management and community service)
= (4/11) + (5/6) - (4/11)*(5/6) = 59/66.
This probability can aslo be calculated as 1 – probability that he has neither completed comunity service not has taken data management.
= 1 – (7/11)*(1/6) = 59/66