gistfile1.md

Weight	Pairs
10 pounds	1
15	1
25	1
55	2

Given:

• Dan, Travis and Kyle can benchpress an average of 280 pounds
• Dan benchpresses 315 pounds.
• Travis bencpresses 20 pounds less than Dan
• 3 pairs of weights are chosen at random from the given 5 pairs
• weight of the bar on which weights are loaded = 45 pounds
• FIND probability that Kyle can't lift the randomly chosen weights but Dan and Travis can

Solution:

• From Statement 1, (Dan + Travis + Kyle)/3 = 280
• From Statement 2, Dan = 315
• From Statement 3, Travis = 315 -20 = 295 pounds (can benchpress)
• From the above we finally get Dan = 315, Travis = 295 and Kyle = 230.
• Now removing the weight of the bar from what these three can lift, we get Dan = 315-45 = 270; Similarly Travis = 250 and Kyle = 230-45 = 185.
• So the probability that Kyle can't lift the weight but Dan and Travis can is P(185 < X <= 250). i.e 250 is the upper limit because we want both Dan and Travis to be able to lift it.
• Out of 5 pairs we are choosing 3 pairs randomly so the possible ways are 5C3 = 5!/(3! * 2!) = 10 combinations.

Weight Combination	Total Weight of the Pairs
10,15,25	(10+15+25) * 2 = 100 {Since pair of weights}
10,15,55	(10 + 15 + 55) * 2 = 160
10,15,55	160
10,25,55	180
10,25,55	180
15,25,55	190
15,25,55	190
25,55,55	270
15,55,55	250
10,55,55	240

• NOTE: There are two 55 pound pairs so combinations with 55 can occur twice in the above table.
• Out of the 10 combinations, there are 4 combinations where the total weight lies between 185 and 250 i.e 190,190,250 and 240.
• Therefore P(185 < X <= 250) = 4/10 = 2/5