Question

1. When we work with probabilities, we always use the decimal form. What's the decimal version of 15%? (Put a zero before the decimal point.)

2. What about the decimal version of 0.3%? (Put a zero before the decimal point.)

3. Suppose you roll a six-sided die and flip two coins. What is the chance that the die will come up as a 5 or a 6 and you'll get two tails?

Express your answer as a value between 0 and 1, rounded to two decimal places.

4.Suppose you roll a six-sided die and flip three coins. What is the chance that the die will come up as an even number and you'll get at least one heads?

Express your answer as a value between 0 and 1, rounded to two decimal places.

5. Jerry and George are writing a pilot for a sitcom. They estimate they have a 90% chance of the show not being picked up as a series. If that happens, their combined profit is -$40,000 as they've invested a great deal of time and energy and received nothing for it. If the show is picked up, the profit the pair would earn depends on the success of the show, as indicated in the table below. Calculate Jerry and George's expected profit, in thousands of dollars. Do not include a dollar sign ($) in your answer.

Success	Probability	Profit, in thousands of dollars
Minor	25%	20
Moderate	70%	100
Major	5%	500

Answer 1

Decimal version of 15% = 0.15

The decimal version of 0.3%=0.003

4. Bith the events are independent. Thus we can calculate the probability of each event one by one and multiply it to obtain the required probability.

P(die will come up as an even number) = 3/6 = 0.5

P(at least one heads in three flip of coins) = 1-P(no heads) = 1- 0.5³=0.875

Thus the probability that the die will come up as an even number and you'll get at least one heads = 0.5*0.875=0.4375

5. Expected value if the show is spiked up = 0.25*20 + 0.7*100 + 0.05*500 = 100. Thus the profit is $100,000

and expected value if the show is not picked = -$40,000

Given that there is a 90% chance that the show not being picked up as a series. Thus the overall expected profit is:

0.1*100,000 -0.9*40,000 = -$26,000. Thus they are expected to loose $26,000