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- 2. A box contains three fair coins, and two trick coins that have heads on both sides. (a) What is the probability that a randomly selected coin from the box will come up heads when flipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is the probability that it's one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box is flipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes, or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?A coin is flipped 10 times in a row. a. What is the probability that it lands heads up exactly 8 times? b. What is the probability that it lands heads up at least 8 times? c. What is the probability that it lands heads up at most 8 timesA box contains three fair coins, and two trick coins that have heads on both sides.(a) What is the probability that a randomly selected coin from the box will come up heads whenflipped? (b) Suppose you randomly pick a coin from the box and flip it, and it comes up heads. What is theprobability that it’s one of the trick coins? (c) Let X be the random variable that represents the number of heads when every coin in the box isflipped. What is the probability distribution of X? (Hint: you can try counting all the outcomes,or you can remember that coin flips are independent of each other.) (d) What is the expected number of heads when all the coins are flipped?Page 2
- Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.1. A coin is flipped four times. Assume all outcomes are equally likely. What is the probability that there are at least two consecutive flips that come up heads? 2. A hand of 5 cards is drawn from a standard deck of 52 cards. Assume all outcomes are equally likely. What is the probability that at least two of the cards have the same rank? Hint: Find the probability of the complement.The chaper is Probability.
- correctly explain this.last time incorrect solution given.downvote and report solution Q)A set of eight cards contains one joker. Player A and Player B are playing card games with these 8 cards. Player A chooses 5 cards at random, Player B takes the remaining three cards. What is the probability that Player A has the joker? Player A discards 4 cards and Player B discards two cards. It is know that the joker has not been discarded, what is the probability that Player A has the joker?Problem 1. You are playing a version of the roulette game, where the pockets are from 0 to 10and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability th at you get a total of 17 given on the first spin you spin a 2? What about a 3? Solve by simulation and analytically.There are 7 balls hidden in a box (3 blue and 4 green). If you first select a green ball and do not replace in the box, what is the probability that the second ball you select from the box will also be green? [Your answer can be written either as a fraction or decimal]
- When correctly adjusted, a machine that makes widgets operates with a 5% defective rate. However, there is a 10% chance that a disgruntled employee shakes the machine, in which case the defective rate jumps up to 30%. Q4Probability and Statistics Consider the following experiment. You draw a square, of width 1 foot, on the floor. Inside the square, you inscribe a circle of diameter 1 foot. The circle will just fit inside the square. You then throw a dart at the square in such a way that it is equally likely to fall on any point of the square. What is the probability that the dart falls inside the circle? (Think about area!)How might this process be used to estimate the value of π?A card is drawn from a well shuffled deck of cards. What is the probability that the card will be a face card?a. 1/2b. 1/4c. 10/13d. 1/26