Discrete vs Continuous
Probability Distributions
Probability
P(A and B)
P(A or B)
100
The difference between discrete and continuous variables?
What is discrete=countable, continuous= not countable
100
The probabilities in a probability distribution should add up to what?
What is one.
100
Probability of getting tails on a coin toss.
What is 1/2 or 50%
100
There is four pieces of candy in your pocket. One is a Twix bar, two are Snickers, and one is a Kitkat. What is the probability you reach into your pocket and randomly select and eat a Twix bar and then a Kitkat?
What is (1/4) * (1/3) = (1/12)
100
A spinner has an equal chance of landing on each of its seven numbered regions. After spinning, it lands in region four or five
(1/7) * (1/7) = (1/49)
200
The speed of a race car in mph.
What is continuous.
200
Is the following a probability distribution? x: 1 2 3 4 p(x): .23 .32 .45 .07
What is no because the probabilities do not add up to 1.
200
The probability of getting a black face card in a deck of cards
What is 6/52 = 3/26 or 0.1154(rounded 4 decimal places)
200
A magic bush has 30 blueberries, 20 raspberries, and 16 blackberries. What is the probability you randomly select and eat a blueberry and then a blackberry?
What is (30/66) * (16/65) = 480/4290 =16/143
200
If you roll a die, what is the probability you roll a number divisible by 2 or 4?
What is (3/6) + (1/6) - (1/6) = (3/6)
300
The number of math majors at USC.
What is discrete.
300
A box contains 3 markers, 2 pens, 1 crayon, and 1 sharpie.
Define the variable and construct a probability distribution.
Let x be the kind of writing instrument
x: marker pens crayon sharpie
P(x): 3/7 2/7 1/7 1/7
300
Three coins are tossed up in the air, one at a time. What is the probability that two of them will land heads up and one will land tails up?
What is 3/8 or 0.375
300
You have five shirts planned out to wear for the week. Two are red, one is black, one is blue, and the other is white. You randomly select two shirts for Thursday and Friday. What is the probability you select a red shirt for each day?
What is (2/5) * (1/4) = 2/20=1/10 or 0.1
300
The probability of choosing a red or blue shirt out of a selection of three green shirts, two red shirts, a blue shirt, or four yellow shirts.
What is (2/10) + (1/10) = (3/10)
400
The number of people that play the NH Lottery each day.
What is discrete.
400
Below is a probability distribution for the number of math failures of BC students. x: 0 1 2 3 4 P(x): .41 .20 ? .08 .20 Find the missing probability and find P(x <3).
What is P(2)= 0.11 P(x<3)= .72
400
A bag contains 14 blue, 6 red, 12 green, and 8 purple buttons. 25 buttons are removed from the bag randomly. How many of the removed buttons were red if the chance of drawing a red button from the bag is now 1/3?
What is 1
Steps:
1. 40(total # of B)-25=15 buttons left
2. So, for finding the number of red buttons in the bag after removing we can write,
n(A) = p(A) × n(S) (A is the event of drawing the number of red buttons and p(A) = 1/3 and n(s) = 15 (after removing) )
the number of red buttons in the bag after removing = × 15 = 5
3. the number of red buttons left in the bag = 5
then, the red buttons removed from the bag = 6 - 5 = 1
400
A bag has eight marbles in it. There are two green marbles, four yellow marbles, 1 red marble, and 1 blue marble. You randomly grab a marble and then select another marble, putting the marble back in the bag. You select a green marble both times.
(2/8) * (2/8) = (4/64=1/16) 0.0625
400
A bag contains seven green jerseys numbered one to seven and six purple jerseys numbered one to six. You randomly pick a jersey. It is green or a number less than two.
(7/13) + (2/13) - (1/13) = (8/13)
500
The number of cups of coffee that SpeedyUrchin drinks each day.
What is continuous or discrete.
500
Using your graphing calculator, find the mean for the following probability distribution: x: 0 1 2 3 4 5 6 P(x): .04 .26 .36 .20 .08 .04 .02
Mean = multiply each value of X by each probability P(X) , Add the results from step 3 together
What is mean=2.22
500
A pouch has 8 red marbles, 10 blue marbles and 7 yellow marbles. What has a greater probability, getting blue marbles, or getting either a red or yellow marble?
What is getting a red or yellow marble (15/25=3/5 or 60%)
500
A box contains seven balls in it. If there is one basketball, two soccer balls, three tennis balls, and one more basketball in it, what is the probability you select a basketball and then a soccer ball without replacing the basketball?
(2/7) * (2/6) = (4/42=2/21)
500
If there are fourteen papers, and seven are green and seven are blue, and each individual are numbered 1 to 7 and 8 to 14, what is the probability of choosing a green paper or a number divisible by three?
What is (7/14) + (4/14) - (2/14) = (9/14)