Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.   A glass manufacturer finds that 1 in every 1000glass items produced is warped. Find the probability that​  (a) the first warped glass item is the 11th item​ produced,   (b) the first warped item is the​ first, second, or third item​ produced,    (c) none of the first 10 glass items produced are defective. ​ ​(Round to three decimal places as​ needed.)

In a jury trial, suppose the probability the defendant is convicted given guilt, is 0.95, and the probability the defendant is acquitted given innocence is 0.95. Suppose 90% of defendants are truly guilty. Given that the defendant is convicted, find the probability that he was actually guilty.

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. Assume the probability that you will make a sale on any given telephone call is 0.17. Find the probability that you (a) make your first sale on the fifth call, (b) make your sale on the first, second, or third call, and (c) do not make a sale on the first three calls. (a) P(make your first sale on the fifth call) =| (Round to three decimal places as needed.)

Based on a​ survey, assume that 27​% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly​ selected, exactly two of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

Based on a​ survey, assume that 44​% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly​ selected, exactly three of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

An urn contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given below. Number of red marbles 0 1 2 3 Probability 1/8 3/8 3/8 1/8 For this distribution, the probability of 2 or more red marbles is given by:   a. 1/4.   b. 3/8.   c. 6/8.   d. 1/2.

A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X P(X = x) 2 0.015 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)

The probability that a child will like a new flavor of ice cream is 0.72. In a group of nine children find the probability that at least 7 children like the new flavor.

A company receives 30% of its shipments from source A and the rest from source B. For source A, the defective rate is 10% and for source B, the defective rate is 6%. The company just receives a shipment which contains 10 items.Determine the probability that there will be one defective item.