Question

1) A raffle offers one $1000.00 prize, one $500.00 prize, and five $200.00 prizes. There are 5000 tickets sold at $4 each. Find the expectation if a person buys one ticket.

2) In a large bag of marbles, 35% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly two red marbles?

3) In a survey, 65% of the voters support a particular referendum. If 10 voters are chosen at random, find the standard deviation of the number of voters who support the referendum.

4) 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?

Answer 1

1. If X denotes the amount won in a game then:

2. If X denotes the number of red marbles among the 4 marbles chosen, then X follows a Binomial distribution with n=4 and p=0.35. Thus:

3. If Y denotes the number of voters who supports the referendum, then Y follows a Binomial distribution with n=10 and p=0.65. Hence Standard deviation of Y is

4. As the student has to select the last question thus he has 4 questions to select from the remaining 11 questions. Thus the number of ways in which student can select five questions from the exam: