A scientist has three beakers which are 1/3 full, 1/2 full and 5/6 full. She needs to add one more beaker to conduct her experiment. If she wishes the four beakers to have be a mean of 2/3 full, how full should the last beaker be exactly?
The answer is completely full (or 1). Since the mean needs to be 2/3 (or 4/6) for four beakers, the first step is to multiply 4/6 full x 4 beakers = 16/6 total for four beakers. Then add the three existing beakers, which equals 2/6 full + 3/6 full + 5/6 full = 10/6 total for first three beakers. Then subtract the total for three beakers from the total for four beakers to get the answer. 16/6 - 10/6 = 6/6 (or 1).
A couple has six children. What are the odds of them having at least one girl among the six? Assume the chances of having a boy/girl are equal at 50/50.
The answer is 1 - (0.50)^6 = 98.44%. Since the question specifies AT LEAST one girl, you first have to find the odds that all six kids are boys - this is the only situation in which there would be zero girls among the six. This is represented by 50%^6. Then subtract that answer from 100% (or 1) to reach the answer.
I like to explain accounting concepts using simple examples from life. Under the accrual basis of accounting, when exactly do you become less wealthy in the following situation - going to the bar and purchasing a beer on credit?
You become less wealthy once you actually drink the beer. When you purchased the beer, you simply purchased an asset. You did this on credit, which is a promise to pay in the future (a liability). Therefore, the balance sheet balances through an increase of the assets matching the increase in liabilities; this means residual equity (wealth) is neither created nor destroyed in the transaction. Only when you drink the beer does the asset start losing value (depreciation expense). This expense shows up in the Income Statement reducing Net Income and thus reducing Retained Earnings (which is equity).