Tutor profile: Joshua S.
Explain "There's no such thing as a free lunch".
This is a fundamental economics concept that attempts to explain that nothing is free. People never get something for nothing, there are always opportunity costs. For example if there is a free lunch somewhere, you would have to drive or walk there and spend your time eating that lunch. You could be doing other things with your limited time. There may not be a monetary cost involved with the lunch but there are opportunity costs that must be considered. By consuming the free lunch you are agreeing to trade-offs involving your time and other potential dining opportunities.
A coin is flipped 4 times. What is the probability of getting one tails and three heads?
This question involves us calculating the probability of an outcome occurring. In this case the outcome is getting one tails and three heads after flipping the coin 4 times. When flipping a coin we have two possible outcomes: heads and tails. Provided the coin is fair, the probability of getting head or tails should be 50% for both. Here are the possible outcomes for this game: (H = heads, T = tails) HHHH, THHH, HTHH, HHTH, HHHT, HTTH, TTHH, THHT, THTH, HHTT, HTHT, TTTT, TTTH, TTHT, THTT, HTTT, An easier way to get the total number of outcomes is by solving the following (2)^4 = 16. 2 is the number of possible results, heads or tails, and the 4 is the number of times we tossed the coin. So we have 16 possible results and we want to find the number of times where we get one tails and three heads. By simply looking at our results we can see that this happens 4 times. If a result occurs 4 times after 16 trials then the probability of that event occurring is 4/16 or 25%. 25% would be our answer to this question. We can also solve this problem by using the binomial formula. P(x) = n!/((n-x)!x!) * P^x * (1-P) ^ (n-x) N is the total number of times we flip the coin, 4 x will be the number of heads we get after flipping the coin N times, 3 P is the probability of getting heads after flipping the coin, .50 Now let's plug these values into our formula P(x) = 4!/((4-3)!*3!) * (0.5)^3 * (0.5)^1 = 4!/(1 * 3!) * (0.5)^3 * 0.5 4! = 4*3*2*1 = 24 3! = 3*2*1 = 6 P(x) = 24/6 * (0.5)^3 * 0.5 = 4 * .125 * 0.5 = 0.25 or 25% This is what we got earlier using our previous method. Sometimes it is easier to write out all of the possible outcomes like we did initially. Other times, for instance if we flip the coin 60 times, it is much easier to use the formula than to try and write out all the possible outcomes.
If an investor put $10,000 in a checking account with a 2% interest rate compounded annually, how much would that investor have after 30 years?
This question involves a concept called the time value of money. The formula, Future Value = Present Value x (1 + rate) ^ number of periods, is what we will use to solve this question. Let's first identify the variables in this scenario. Our present value, what we have today, is $10,000. We have an interest rate of 2% and the number of periods is 30. We do not know what the future value is, that is what we will be attempting to solve. Now let's plug in our values into our variables in the time value of money equation. Future Value = $10,000 * (1 + .02) ^ 30 = $18,113 The investor will have $18,113 in their checking account after 30 years provided the interest rate remains constant and the bank remains solvent.
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