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 Five cards are randomly dealt from a standard deck. Show the probability distribution of the number of cards dealt that are either face cards or aces.
 

In how many different ways can a true-false test
consisting of 9 questions be answered?

In a normal curve, the area between z=-1 and z=1 is equal to?

How's to solve question such as 64 bulb  is the result of random sampling , determine the probability that the mean time to failure will exceed 820 hours

 

An event has the probability 𝑝 = 3
8
. Find the complete binomial distribution for 
n=5 trails. 
 

In a survey, 70% of men and 55% of women said that they smoked. If the proportion of men to women is 60:40 and a person from the survey was chosen at random and found to be a smoker, what is the probability that this person is a woman?

A certain machine is operating using three components C1, C2 and C3. The probabilities of these three components to perform well are respectively.0.4, 0.3 and 0.6 Suppose that these components work independently, find the probability that only two component work properly
 

eighty percent of the employees at the General mills' plant have their bimonthly wages sent by electronic transfer. suppose a researcher selects randomly seven employees and counts the number using direct deposit. What is the probability that all seven employees use direct deposit?

Sally has caught covid but doesn’t know it yet. She is testing herself with rapid antigen kits which have an 80% probability of returning a positive result for an infected person. For the purpose of this question you can assume that the results of repeated tests are independent. 

a) If sally uses 3 test kits what is the probability that at least one will return a positive result? 

b) In 3 tests, what is the expected number of positive results?

c) Sally has gotten her hands on more effective tests, these ones have a 90% probability of returning a positive result for an infected person. If she tested herself
twice with the new tests, how many positive results would she expect to see?

Sally has caught covid but doesn’t know it yet. She is testing herself with rapid antigen kits which have an 80% probability of returning a positive result for an infected person. For the purpose of this question you can assume that the results of repeated tests are independent. 

a) If sally uses 3 test kits what is the probability that at least one will return a positive result? 

b) In 3 tests, what is the expected number of positive results?

c) Sally has gotten her hands on more effective tests, these ones have a 90% probability of returning a positive result for an infected person. If she tested herself
twice with the new tests, how many positive results would she expect to see?

Sharon draws a random card, from a regular deck of cards, and rolls a regular 6 sided die. What is the probability that Sharon draws a card that is a Heart and rolls a 3?

Consider an electric refrigerator located in a room. Determine the direction of the work and heat interactions (in  or out) when the following are taken as the system: 

(a) the contents of the refrigerator,  

(b) all parts of the refrigerator including the contents, and  

(c) everything contained within the room during a winter day. 

A simple binary communication channel carries messages by using two signals 0 and 1. It was assumed that for a given binary channel, 40% of the time a 1 is transmitted; the probability that a transmitted 0 is correctly received is 0.90 ; the probability that 1is correctly received 0.95. This information is illustrated in Figure 1 where
     A = event that A = event that B = event that B = event that
1 is 0 is 1 is 0 is
transmitted. transmitted.
received. received.

Four coins are tossed 160 times. X denotes the number of heads. The observed 
frequencies are also given in the following table. Fit a binomial distribution 
assuming that the coins are unbiased.
X: Number of heads 0 1 2 3 4
Observed frequency 8 34 69 43 6
 

A large cooler contains the following drinks: 6 lemonade, 8 Sprite, 15 Coke, and 7 root beer. You randomly pick two cans, one at a time (without replacement).

(a) What is the probability that you get 2 cans of Sprite?

(b) What is the probability that you do not get 2 cans of Coke?

(c) What is the probability that you get either 2 root beer or 2 lemonade?

(d) What is the probability that you get one can of Coke and one can of Sprite?

(e) What is the probability that you get two drinks of the same type?

(1 point) A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood. The device is not totally reliable: 7 % of drivers who have not consumed an excess of alcohol give a reading from the breathalyser as being above the legal limit, while 10 % of drivers who are above the legal limit will give a reading below that level. Suppose that in fact 14 % of drivers are above the legal alcohol limit, and the police stop a driver at random. Give answers to the following to four decimal places.

Part a)
What is the probability that the driver is incorrectly classified as being over the limit?


Part b)
What is the probability that the driver is correctly classified as being over the limit?


Part c)
Find the probability that the driver gives a breathalyser test reading that is over the limit.


Part d)
Find the probability that the driver is under the legal limit, given the breathalyser reading is also below the limit.