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Multiple basic probability problems

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I am having issues resolving some of my homework and need an extra help:
1. A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is 2/3. If there are 18 green marbles in the jar, how many red marbles are there in the jar
2. Find the probability of selecting a heart or an 8 when a single card is drawn from a standard deck
3. According to the Beer Brokers of America, 80% of adults in the United States enjoy drinking beer. Choose a group of 4 adult US citizens at random. The probability that all of them enjoy drinking beer is
4. At the local YMCA, 20% of the members use the tread mills, 40% of the members
lift weights, and 20% of the members swim laps. If 5% of the members lift weights and swim, find the probability that a member lifts weights, given that they also swim
5. A toy store manager wants to arrange 4 different sizes of toy trucks in a row. How many ways can this be done
6. If a menu has a choice of 3 appetizers, 3 main courses, and 4 desserts, how many dinners are possible if each includes one appetizer, one main course, and one dessert
7. Five college engineering students are choosing specialized fields of engineering to study. Each student is allowed to select one field. The available fields are Electrical Engineering (EE), Mechanical Engineering (ME), and Computer Engineering (CE). If the second student does not meet the requirements for ME and the third student does not meet the requirements for CE, then how many ways are there for the students to choose an engineering field
8. How many ways can a student select five questions from an exam containing 12
questions, if one of the five must be the last question
9. A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
10. If 25 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets

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Solution Preview

HI there,

Thanks for allowing me to work on your question. Here are my answers:

1. According to the probability of a red marble 2/3, the ratio between red and green is 2:(3-2)=2, therefore the red marble number is 18x2=36.

2. hearts: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
clubs: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
spades: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
diamonds: 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, A
the number of picking up ...

Solution Summary

The solution provide detailed explanations for multiple probability problems.