# Lofty Goals

Joseph is the sales manager of a large company. Each of his four sales reps turned in their goals for the fourth quarter and coincidentally, they all turned in a goal of 1 Million in sales. Based on the past five years, Joseph knew that each rep had the following chance of hitting that goal:

Mel had an 80% chance of hitting his goal of 1 Million dollars. Randy had a 75% chance of hitting his goal, Jimmy had a 70% chance and Tim had a 60% chance. Based on these statistics, what is the probability that all four reps hit their goal for the fourth quarter?

a)     100%

b)     72.5%

c)     55.5%

d)     25.2%

### 5 guesses to Lofty Goals

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• anant

The probability actually works out to 71.25%. I’ll go for option (b) since that is the nearest to the answer

• Gabrielle

The answer is none of them, it’s 71.25, but since b is pretty close, I say b or my own answer 71.25

• Dude

Both are incorrect, keep trying.

• Nanao Ise

The probability of that would be d) 25.2 percent.

Personally, I’m kinda confused about why it is so, but it’s something that seems, in a way, relevant and sensible.

It’s basically viewed as a fraction, as 80 out of 100, times 75 out of 100, times 70 out of 100, times 60 out of 100.

You merely have to take each of the sales representatives’ probability rates and multiply them by each other – which gets you the number of 25,200,000.

Then you multiply the denominators – all four 100’s, then giving you 100,000,000.

Divide and simplify until reaching a percentage.

• Dude

Yes Nanao Ise, it can be confusing, but you are correct.

The answer is D: 25.2%. It’s easy to figure the average of the four reps, which would be 72.5% but that would be wrong.

If we wanted to know the probability of Mel we already know it’s 80%. So the probability of Mel and Randy (75%), BOTH hitting their goals is 75% of 80% or 60%. For Mel, Randy and Jimmy (70%) it would now be 42% and including Tim would be 60% of 42% which is: 25.2%.

You are today’s winner.