- A fair coin is tossed 5 times. What is the probability of getting at most 4 tails?
1- (1/2)^3
- When you roll a pair of dice, a double is when both dice show the same number, e.g. both show '1' or both show '4'. What is the chance of a double when you roll a pair of dice?
5/36
- The game Monopoly is played by rolling a pair of dice. If you land in jail, then to get out, you must roll a double on any one of your next three turns, or else pay a fine. What are the chances that you get out of jail without paying a fine?
1-(5/6)^3
- 3% of all applicants to the Stanford Medical School are admitted. 70% of all applicants have a GPA of 3.6 or above. Of those who are admitted, 95% have a GPA of 3.6 or above. What are the chances of being admitted for an applicant whose GPA is 3.6 or above?
P(admit) = 3%, P(GPA) = 70%, P(GPA|admit) = 95% P(admit|GPA) = P(GPA|admit) * P(admit) / P(GPA) = 0.95 * 0.03 /0.07
- A multiple choice exam has 10 questions. Each question has 3 possible answers, of which one is correct. A student knows the correct answers to 4 questions and guesses the answers to the other 6 questions. It turns out that the student answered the first question correctly. What are the chances that the student was merely guessing?
P(correct) = 4/10 * 1 + 6/10 * 1/3, P(guess) = 6/10, P(correct|guess) = 1/3 P(guess|correct) = P(correct|guess) * P(guess) / P(correct) = (1/3 * 6/10) / (4/10 * 1 +6/10 * 1/3)
- There are three boxes on the table: The first box contains 2 quarters, the second box contains 2 nickels, and the last box contains 1 quarter and 1 nickel. You choose a box at random, then you pick a coin at random from the chosen box. If the coin you picked is a quarter, what's the chance that the other coin in the box is also a quarter?
P(q/qq) = 1, P(q/qn) = 1/2 p(qq|q) = p(q|qq) * P(qq)/P(q) = P(q|qq) * P(qq) / P(q|qq) * 1/3 + P(q|qn) * 1/3 = (1 * 1/3 )/(1 * 1/3 + 1/2*1/3)