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Hi,
Could someone please help me out with the below question. It is Q195 from Kaplan exam kit.A company has estimated the selling prices and variable costs of one of its products as follows:
Selling price per unit:
$ Probability
40 0.30
50 0.45
60 0.25Variable cost per unit:
$ Probability
20 0.55
30 0.25
40 0.20the company will be able to supply 1,000 units of its product each week irrespective of the selling price. Selling price and variable cost per unit are independent of each other.
The probability that the weekly contribution will exceed $20,000 is _______?
Hi
For this you need to start by listing all the possible combinations of selling price and variable cost that together earn a contribution greater than $20 …
i.e.
SP 50 less VC $20 = $30
SP 60 less VC $20 = $40
SP 60 less VC $30 = $30Then for each case you need to find the probability of the selling price occurring multiplied by the probability of the variable cost occurring .. i.e. the first in list,,, 50 less 20 ( there is a probability of 0.45 that selling price will be 50… and a probability of 0.55 that vc will be 20 so in that instance the probabilities of them happening together are 0.45 * 0.55 = 0.2475 … so a 24.75 chance of that selling price of 50 and that variable cost of 20 occurring together…. You continue to do the same for the others in the list. Then the sum of all the combined probabilities gives you the chance of any one of them happening i.e.
SP 50 less VC $20 = $30 = 0.45*0.55 = 0.2475
SP 60 less VC $20 = $40 = 0.25*0.55 = 0.1375
SP 60 less VC $30 = $30 = 0.25*0.25 = 0.0625Add them all together 0.2475+0.1375 +0.0625 = 0.4475
this tells us that there is a 44.75% chance that any of those combinations of SP and VC will occur.. ( all of which would earn contribution greater than $20).
Hope that helps
Cath
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