Math 2000 - Solution 1

Spring 2001

1. If you interpret the statement to mean that 75 nurses play at least soccer and 50 nurses play both soccer and softball, it follows that 25 nurses play soccer only. Similarly, if 95 nurses play at least softball and 50 nurses play both soccer and softball, it follows that 45 nurses play softball only. These figures are shown in the Venn diagram below. It is evident that we have already accounted for more than 100 nurses! So the survey must have an error.

	Softball	Soccer

If you interpret the statement to mean that 75 nurses play only soccer, 95 play softball only and 50 play both, then we have accounted for 220 nurses! Again, the survey cannot be accurate.

2a. It’s not clear whether there were 350 people on both jets combined or 350 people on each jet.

2b. It’s not clear whether there were 2.9 million incidents in 1988 or in 1993.

3a. The table below summarizes your options.

	Plan A	Plan B	Savings (B - A)
Go	$1600	$2900	$1300
No Go	$400	$0	-$400

If you travel, you save $2900 - $1600 = $1300 with Plan A (or you lose $1300 with Plan B).

3b. If you do not travel, you save $400 with Plan B (or you lose $400 with Plan A).

3c. Because $1300 is roughly three times greater than $400, you might argue that if your chances of traveling are 1 in 3 or better, then you should choose Plan A.