12 H.W(3) The following circuit operates only if there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that devices fail independently. What is the probability that the circuit is not operating? 0.95 0.90 b

On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form the price of an appliance. If the contestant is correct, he or she wins the appliance. What is the probability of winning when the contestant knows that the price is at least $400?

If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on yellow.

The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.

Suppose a weather report indicates that the probability of rain this week is 0.20. This week Next week According to the report, if it rains this week, then the probability of rain next Rain week is 0.33. If it does not rain this week, then the probability of rain next week is 0.17. The tree diagram models this weather report. 0.33 Rain 0.20 Determine the probability that it will not rain for the next two weeks. Express 0.67 No rain your answer as a decimal precise to two decimal places. Rain 0.17 probability = 0.80 No rain 0.83 No rain

Each sample of water has a 10% chance of containing a particular organic pollutant.  Assume that the samples are independent with regard to the presence of the pollutant. Approximate the probability that, in the next 200 samples, there are 20 to 25 samples contain the pollutant. You can use Excel to calculate. (x.xxxx)

A hockey player is to take 3 shots on a certain goalie. The probability he will score a goal on his first shot is 0.3. If he scores on his first shot, the chance he will score on his second shot increases by 0.1; if he misses, the chance that he scores on his second shot decreases by 0.1. This pattern continues to on his third shot: If the player scores on his second shot, the probability he will score on his third shot increases by another 0.1; should he not score on his second shot, the probability of scoring on the third shot decreases by another 0.1. A random variable X counts the number of goals this hockey player scores. (a) Complete the probability distribution of X below. Use four decimals in each of your entries. X P(X = x) (b) How many goals would you expect this hockey player to score? Enter your answer to four decimals. E(X)= 1 2 3 (c) Compute the standard deviation the random variable X. Enter your answer to two decimals. SD(X) =