Probability and Statistics

How many Powerball tickets would you need to buy to get 50% odds of winning $50,000 ?

• 500

• 4565

• 22,828

• 456,565

One card is selected at random from the following set of 6 cards, each of which has a number and is black (B) or white (W): {2 W,4 W,8 B,8 B,5 W,5 B}

Let B be the event that the selected card is black symbol, and F be the event that the selected card has a 5.

If the probability of drawing a card that is black, P(B) = 1/2

And the probability of drawing a 5, P(F) = 1/3

What is the probability of drawing a card that is black and is a 5, P(B and F) = ?

Select the following true statement:

• 50%

• 33%

• 83%

• 17%

What is the range and median of the box plot?

• range is 80 and median is 30

• range is 40 and median is 50

• range is 100 and median is 30

• range is 80 and median is 50

One popular way to study probability is to roll dice. A standard die has six sides printed with little dots numbering 1, 2, 3, 4, 5, and 6. If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on. The probability table of rolling two dice is above:

Two six-sided dice are rolled. What is the probability that the sum of the two dice is seven? Are these results considered Experimental Probability or Theoretical Probability?

• 1/3 and Theoretical probability

• 1/6 and Theoretical probability

• 7/36 and Experimental probability

• 6/18 and Experimental probability

Each student in a random sample of seniors at a local high school participated in a survey. These students were asked to indicate their gender and their eye color. The table above summarizes the results of the survey:

Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male or has blue eyes?

• 40/110

• 40/80

• 110/200

• 150/200

On April 15, 1912, the Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarized in the table above:

If one of the passengers is randomly selected from the first class passengers, what is the probability that this passenger survived? (That is, what is the probability that the passenger survived, given that this passenger was in first class?)

• 201/324

• 201/1317

• 201/500

• 500/1317

Calculate the percentage decrease in home prices from 2014 to 2015.

• 112.7%

• 88.7%

• -11.3%

• -14.1%

To be recommended for a scholarship at UCA, a student must score above the median of all the students in his or her final year and have a mean mark of at least 90 percent. Delores is hoping for a recommendation with the above marks:

The median mark for the graduating students is 86.5. How many percentage points above the required minimum mean score did Delores score?

• 1.6

• 5.1

• 3.5

• 8.0

The Archer basketball team scored the following for its first 8 games: 51, 67, 55, 70, 53, 74, 58, and 49. Determine the mean, median for that series of numbers.

• mean of 57.6 and median of 55

• mean of 59.6 and median of 58

• mean of 59.6 and median of 56.5

• mean of 59.6 and median of 55

There are four red envelopes, four blue envelopes, and four $1 bills, which will be placed in four of the eight envelopes. Define the event A as “you pick a lucky envelope (one that has a $1 bill in it)” and event B as “you pick a blue envelope”. Suppose one $1 bill is placed in a blue envelope, and the three remaining $1 bills are placed in three red envelopes.

If you know that the envelope you picked is blue, what is the probability that you picked a lucky envelope? Write this probability symbolically using letters A and/or B.

• P(A) = 1/2

• P(B) = 1/2

• P(A) = 3/4

• P(A) = 1/4