Question 568292: Hi. Can you please help me with this question!!!
Sixty percent of a company's sales representatives have completed training seminars. Of these, 80 percent have had increased sales. Overall 56 percent (whether trained or not) have had increased sales. What's the probability of increased sales given that the representative has not been trained?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 60% of the sales force has completed sales training.
of these, 80% have increased sales.
overall 56% have increased sales.
what is probability of increased sales if sales person didn't receive sales training.
the way i see this .....
60% received sales training and 80% of these increased sales.
this makes 80% of 60% = 48% of all the sales people have received sales training and increased sales.
since overall 56% of the sales people have increased sales, then the difference is 56% minus 48% = 8% of the sales people have not received sales training and increased sales.
since 40% of the sales people have not received sales training, then 8% of the total divided by 40% of the total means that 20% of the sales people who have not received sales training have increased sales.
your answer should be 20% of the sale people increased sales given that they did not receive sales training.
we can test this out.
assume there are 100 sales people.
60% of them received sales training which means that:
60 received sales training.
40 did not.
80% of the ones who received sales training increased sales.
that makes .8 * 60 = 48 sales people increased sales and received sales training.
overall 56% of the sales people increased sales.
that means that 56 people increased sales.
56 increased sales and 48 of these received sales training leaving 8 that increased sales and didn't receive sales training.
since 40 didn't receive sales training, these 8 represent 8/40 = 20% of the sales people that didn't receive sales training.
numbers check out so we're good so far.
in terms of probability theory:
p(a | b) = p(a intersect b) / p(b)
p(a) is the probability that a sales person increased sales
p(b) is the probability that the sales person did not receive sales training
p(a intersect b) is the probability that the sales person increased sales and did not receive sales training.
we know that p(a) is 56% because that was given.
we know that p(b) is 40% because that was also given.
we deduced that p(a intersect b) is equal to 8% because we calculated that from the data given (56% total sales increase minus 48% sales increase with training leaves 8% sales increase without training).
our formula becomes:
p(a | b) = p(a intersect b) / p(b) = 8% / 40% = .2 which is equal to 20%.
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