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Probability and statistics

by | Nov 30, 2023 | questions

simple introductory questions on probability. I am studying for exam, so write the answer in the boxes provided and EXPLAIN IT BELOW, BRIEF EXPLANATION ON HOW YOU GOT THE ANSWER

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PROBABILITY
If  find:  a)   The odds FOR E.  Answer:  to   b)   The odds AGAINST E.  Answer:  to 
In an experiment, a ball is drawn from an urn containing 11 orange balls and 7 yellow balls. If the ball is orange, three coins are tossed. Otherwise two coins are tossed. 
How many elements of the sample space will have a orange ball ? 
How many elements of the sample space are there altogether ? 
There are five Oklahoma State Officials: Governor (G), Lieutenant Governer (L), Secretary of State (S), Attorney General (A), and Treasurer (T). Take all possible samples without replacement of size 3 that can be obtained from the population of five officials. (Note, there are 10 possible samples!)  (a) What is the probability that the governor is included in the sample?   (b) What is the probability that the governor, attorney general and the treasurer are included in the sample? 
Two six-sided dice are rolled (one red and one green). Some possibilities are (Red=1,Green=5) or (Red=2,Green=2) etc.  (a) How many total possibilities are there? 
For the rest of the questions, we will assume that the dice are fair and that all of the possibilities in (a) are equally likely.  (b) What is the probability that the sum on the two dice comes out to be 9?
(c) What is the probability that the sum on the two dice comes out to be 8? 
(d) What is the probability that the numbers on the two dice are equal? 
5. (Note that an Ace is considered a face card for this problem)  In drawing a single card from a regular deck of 52 cards we have:
(a) P( black or a face card ) =   (b) P( black or a 3 ) =   (c) P( black and a Queen ) =   (d) P( face card or a number card ) =   (e) P( black and a face card ) = 
A card is drawn at random from a regular playing card deck of 52 cards. Find the probability that an ace is drawn.  Answer: 
Employment data at a large company reveal that 52 % of the  workers are married, that 24 % are college graduates, and  that 1/6 of the college graduates are…

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