Definitions/Vocab
What is the definition of simulation?
Imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes
A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes that 5 consecutive reds have occurred and bets heavily on black at the next spin. When asked why, he explains that "black is due." Explain why his reasoning is wrong.
The wheel is not affected by its past outcomes. So on any one spin, black and red remain equally likely to occur.
*Book* pg. 384 #4 (refer to book for table)
a.) What is the probability that the vehicle is a crossover?
b.) Find the probability that the vehicle is not an SUV or a minivan
a.) 1 - 0.46 - 0.15 - 0.10 - 0.05 = 0.24
b.) 0.46 + 0.15 + 0.24 = 0.85
*Book* pg. 381 #105 (refer to the table)
If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1?
a.) 0.10 b.) 0.17 c.) 0.30 d.) 0.50 e.) 0.60
e.) 0.60
What is Conditional probability?
The conditional probability that event A happens given that event B has happened is denoted by P(A/B)
If Aaron tunes in to his favorite radio station at a randomly selected time, the probability that a commercial is playing is 0.20.
a.) Interpret the probability for a long-run relative frequency
b.) If Aaron tunes into this station 5 randomly selected times, will there be exactly 1 time when a commercial is playing? Explain your answer
a.) If he tunes in for a long random sample, 20% of the time a commercial will be playing.
b.) No, random behavior is unpredictable in the short run, but has a regular and predictable pattern in the long run. (20% is the long probability, not the short)
*BOOK* pg. 384 #5 (refer to book for table)
Suppose one person from this sample is randomly selected
a.) Find the probability that the person drives an SUV.
b.) Find the probability that the person drives a sedan or exercises for at least 30 minutes 4 or more times per week
a.) 39/120 = 0.325
b.) 25+20+15+12/120 = 0.60
Suppose a candy maker offers a special box of candies with 20 chocolates that look alike. 14 of the chocolates have soft centers, and 6 have hard centers. Suppose you choose 3 of the candies from the box at random. Find the probability that all three candies have soft centers.
2184/6840 = 0.319
p(1st soft) x p(2nd soft | 1st soft) x P(3rd soft | 1st and 2nd) = 14/20 x 13/19 x 12/18
What is the Multiplication rule for independent events?
If A and B are independent events, the probability that A and B both occur is P(A and B)= P(A n B)= P(A)x P(B)
You read in a book about bridge that the probability that each of the four players is dealt exactly 1 ace is approximately 0.11. This means that
a.) In every 100 deals, each player has 1 ace exactly 11 times.
b.) In 1 million deals, the number of deals on which each player has 1 ace will be exactly 110,000.
c.) In a very large number of deals, the % of deals on which each player has 1 ace will be very close to 11%
d.) In a very large number of deals, the average number of aces in a hand will be very close to 0.11
e.)If each player gets an ace in only 2 of the first 50 deals, then each player should get an ace in more than 11% of the next 50 deals
c.) In a very large number of deals, the % of deals on which each player has 1 ace will be very close to 11%
Harris Interactive reported that 33% of U.S adults believe that finding and picking up a penny is good luck. Assuming that responses from different individuals are independent, what is the probability of randomly selecting 10 U.S. adults and finding at least 1 person who believes that finding and picking up a penny is good luck?
1 - (0.67) ^10 = 0.98177
( 1 - (% of non-believers) ^ amount of people )
You are tossing a pair of fair, 6-sided dice in a board game. Tosses are independent. You land in a danger zone that requires you to roll doubles before you are allowed to play again.
a.) What is the probability of rolling doubles on a single toss of the dice?
b.) What is the probability that you do not roll doubles on the first toss, but you do on the second toss?
a.) 6/36 = 1/6 = 0.167
b.) (5/6)x(1/6) = 0.139