What is the probability that a randomly selected member of the club?

Question

1. Forty percent of the members of the Chicago Charges Track and Field Club participated in 40 % of the events at the recent provincial meet, while 34% entered the field events, and 18% entered both track and field events.

a) Illustrate the club’s entries with a Venn diagram.

b) What is the probability that a randomly selected member of the club

i) entered either a track event or a field event at the meet?

ii) did not, for whatever reason, compete at the meet?

Answer 1

The first part of this problem is worded poorly. In order for the rest of the problem to make sense, I will assume that 40% participated in track events.

a) Your Venn Diagram will show 2 intersecting circles labelled Track and Field. You will have 22% in the Track circle, 16% in the Field circle, and 18% in the area where the 2 circles intersect. The 22% and 16% are because 40% - 18% = 22% and 34% - 18% = 16%. This way, the sum of the probabilities in each of the circles is correct.

b) From the Venn Diagram, you could just add 22% + 18% + 16% = 56%

Alternatively, you can use the formula P(A U B) = P(A) +P(B) - P(A n B) here A n B is supposed to indicate A intersect B

The number not competing is 1 - P(A U B) = 1 - 56% = 44%