<< Chapter < Page Chapter >> Page >

Try it

In a standard deck, there are 52 cards. Twelve cards are face cards ( F ) and 40 cards are not face cards ( N ). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities.

This is a tree diagram with branches showing frequencies of each draw. The first branch shows 2 lines: F 12/52 and N 40/52. The second branch has a set of 2 lines (F 11/52 and N 40/51) for each line of the first branch. Multiply along each line to find FF 121/2652, FN 480/2652, NF 480/2652, and NN 1560/2652.
  1. Find P ( FN OR NF ).
  2. Find P ( N | F ).
  3. Find P (at most one face card).
    Hint: "At most one face card" means zero or one face card.
  4. Find P (at least on face card).
    Hint: "At least one face card" means one or two face cards.
  1. P ( FN OR NF ) = 480 2,652  +  480 2,652  =  960 2,652  =  80 221
  2. P ( N | F ) = 40 51
  3. P (at most one face card) = (480  +  480  +  1,560) 2,652 = 2 , 520 2 , 652
  4. P (at least one face card) = (132 + 480 + 480) 2,652 = 1,092 2,652
Got questions? Get instant answers now!

A litter of kittens available for adoption at the Humane Society has four tabby kittens and five black kittens. A family comes in and randomly selects two kittens (without replacement) for adoption.

This is a tree diagram with branches showing probabilities of kitten choices. The first branch shows two lines: T 4/9 and B 5/9. The second branch has a set of 2 lines for each first branch line. Below T 4/9 are T 3/8 and B 5/8. Below B 5/9 are T 4/8 and B 4/8. Multiply along each line to find probabilities of possible combinations.

  1. What is the probability that both kittens are tabby?
    a. ( 1 2 ) ( 1 2 ) b. ( 4 9 ) ( 4 9 ) c. ( 4 9 ) ( 3 8 ) d. ( 4 9 ) ( 5 9 )
  2. What is the probability that one kitten of each coloring is selected?
    a. ( 4 9 ) ( 5 9 ) b. ( 4 9 ) ( 5 8 ) c. ( 4 9 ) ( 5 9 ) + ( 5 9 ) ( 4 9 ) d. ( 4 9 ) ( 5 8 ) + ( 5 9 ) ( 4 8 )
  3. What is the probability that a tabby is chosen as the second kitten when a black kitten was chosen as the first?
  4. What is the probability of choosing two kittens of the same color?

a. c, b. d, c. 4 8 , d. 32 72

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Try it

Suppose there are four red balls and three yellow balls in a box. Three balls are drawn from the box without replacement. What is the probability that one ball of each coloring is selected?

( 4 7 ) ( 3 6 ) + ( 3 7 ) ( 4 6 )

Got questions? Get instant answers now!

Venn diagram

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event A = {1, 2, 3, 4, 5, 6} and event B = {6, 7, 8, 9}. Then A AND B = {6} and A  OR  B = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The Venn diagram is as follows:

A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.
Got questions? Get instant answers now!

Try it

Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event C = {green, blue, purple} and event P = {red, yellow, blue}. Then C AND P = {blue} and C OR P = {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.

Got questions? Get instant answers now!

Flip two fair coins. Let A = tails on the first coin. Let B = tails on the second coin. Then A = { TT , TH } and B = { TT , HT }. Therefore, A AND B = { TT }. A OR B = { TH , TT , HT }.

The sample space when you flip two fair coins is X = { HH , HT , TH , TT }. The outcome HH is in NEITHER A NOR B . The Venn diagram is as follows:

This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.
Got questions? Get instant answers now!

Try it

Roll a fair, six-sided die. Let A = a prime number of dots is rolled. Let B = an odd number of dots is rolled. Then A = {2, 3, 5} and B = {1, 3, 5}. Therefore, A AND B = {3, 5}. A OR B = {1, 2, 3, 5}. The sample space for rolling a fair die is S = {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.

Got questions? Get instant answers now!

Forty percent of the students at a local college belong to a club and 50% work part time. Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let C = student belongs to a club and PT = student works part time.

This is a venn diagram with one set containing students in clubs and another set containing students working  part-time. Both sets share students who are members of clubs and also work part-time. The universe is labeled S.

If a student is selected at random, find

  • the probability that the student belongs to a club. P ( C ) = 0.40
  • the probability that the student works part time. P ( PT ) = 0.50
  • the probability that the student belongs to a club AND works part time. P ( C AND PT ) = 0.05
  • the probability that the student belongs to a club given that the student works part time. P ( C | P T )   =   P ( C  AND  P T ) P ( P T )   =   0.05 0.50   =   0.1
  • the probability that the student belongs to a club OR works part time. P ( C OR PT ) = P ( C ) + P ( PT ) - P ( C AND PT ) = 0.40 + 0.50 - 0.05 = 0.85
Got questions? Get instant answers now!

Questions & Answers

if the death of of the snow is my yard is normally distributed with the m is equals to 2.5 and what is the probability that a randomly chosen location with have a no that between 2.25 and 2.76
Sakshi Reply
hey
Shubham
🤔
Iqra
hello
Sakshi
hii
Rushikesh
helow
why Statistics so hard
Mohd
ho geya solve
Sakshi
it's not hard
Sakshi
it is hard 😭
Mohd
solution?
Abdul
hii
Aadil
it's just need to be concentrate
Akinyemi
exactly..... concentration is very important
Iqra
rewrite the question
Aadil
what is the true statement about random variable?
Henna Reply
A consumer advocate agency wants to estimate the mean repair cost of a washing machine. the agency randomly selects 40 repair cost and find the mean to be $100.00.The standards deviation is $17.50. Construct a 90% confidence interval for the mean.
Deshah Reply
pls I need understand this statistics very will is giving me problem
Bolanle Reply
Sixty-four third year high school students were given a standardized reading comprehension test. The mean and standard deviation obtained were 52.27 and 8.24, respectively. Is the mean significantly different from the population mean of 50? Use the 5% level of significance.
Daryl Reply
No
Ariel
how do I find the modal class
Bruce Reply
look for the highest occuring number in the class
Kusi
the probability of an event occuring is defined as?
James Reply
The probability of an even occurring is expected event÷ event being cancelled or event occurring / event not occurring
Gokuna
what is simple bar chat
Toyin Reply
Simple Bar Chart is a Diagram which shows the data values in form of horizontal bars. It shows categories along y-axis and values along x-axis. The x-axis displays above the bars and y-axis displays on left of the bars with the bars extending to the right side according to their values.
Muhammad
statistics is percentage only
Moha Reply
the first word is chance for that we use percentages
muhammad
it is not at all that statistics is a percentage only
Shambhavi
I need more examples
Luwam Reply
how to calculate sample needed
Jim Reply
mole of sample/mole ratio or Va Vb
Gokuna
how to I solve for arithmetic mean
Joe Reply
Yeah. for you to say.
James
yes
niharu
how do I solve for arithmetic mean
Joe Reply
please answer these questions
niharu
add all the data and divide by the number of data sets. For example, if test scores were 70, 60, 70, 80 the total is 280 and the total data sets referred to as N is 4. Therfore the mean or arthritmatic average is 70. I hope this helps.
Jim
*Tan A - Tan B = sin(A-B)/CosA CosB ... *2sinQ/Cos 3Q = tan 3Q - tan Q
Ibraheem Reply
standard error of sample
Umar Reply

Get the best Introductory statistics course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask