Expected Value and Binomial Distribution

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14
• 4.67
• 5
• 7.5

If the expected value is negative, are you expected to win?

• yes
• no

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?

• $1

• $0.50

• -$0.50

• $0

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4

A student group sells 500 raffle tickets for $2 each. At the drawing the top prize will be a gift certificate for $100. Second prize will be a $50 gift card and there will be five 3rd prizes, each a $20 gift card. Do you expect to win or lose (on average)? How much?

• lose an average of $5.50

• lose an average of $1.50

• win an average of $2.00

• lose an average of $10.00

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

• 0.962

• 0.132

• 0.831

• 0.250

The American Red Cross says that about 11% of the U.S. population has Type B blood. A blood drive is being held at your school. What is the probability that at least 2 of the first 10 blood donors has Type B blood? 

• 0.088
• 0.697
• 0.214
• 0.303 

In Vietnam, the probability of rain is 70%.  Find the probability of it raining at most 2 days in a week.

• .9712
• 0.0250
• .0287
• .2988

A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what is the probability that at least one tie is too tight?

• 27.0%

• 12.2%

• 73.0%

• 87.8%

Barry Bonds has a career batting average of .298.  What is the probability that he will get on base 6 times in 10 at bats?

• 3.58%
• 5.46%
• 22.67%
• 100%