1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
maw [93]
3 years ago
11

An urn contains three white balls and two red balls. The balls are drawn from the urn, oneat a time without replacement, until a

white ball is drawn. LetXbe the number of the drawon which a white ball is drawn for the first time. Determine the distribution ofX. Verify it isindeed a pmf. What isE(X)
Mathematics
1 answer:
Tpy6a [65]3 years ago
8 0

Answer:

p ( X = 1 ) = 0.6 , p ( X = 2 ) = 0.3 , p ( X = 3 ) = 0.1

Verified

E ( X ) = 1.5

Step-by-step explanation:

Solution:-

- An urn contains the following colored balls:

                       Color                  Number of balls

                       White                            3

                       Red                               2

- A ball is drawn from urn without replacement until a white ball is drawn for the first time.

- We will construct cases to determine the distribution of the random-variable X: The number of trials it takes to get the first white ball.

- We have three following case:

1) White ball is drawn on the first attempt ( X =  1 ). The probability of drawing a white ball in the first trial would be:

              p ( X = 1 ) = ( Number of white balls ) / ( Total number of ball )

              p ( X = 1 ) = ( 3 ) / ( 5 )

2) A red ball is drawn on the first draw and a white ball is drawn on the second trial ( X = 2 ). The probability of drawing a red ball first would be:

      p ( Red on first trial ) = ( Number of red balls ) / ( Total number of balls )

      p ( Red on first trial ) = ( 2 ) / ( 5 )

- Then draw a white ball from a total of 4 balls left in the urn ( remember without replacement ).

   p ( White on second trial ) = ( Number of white balls ) / ( number of balls left )

   p ( White on second trial ) = ( 3 ) / ( 4 )

- Then to draw red on first trial and white ball on second trial we can express:

                p ( X = 2 ) =  p ( Red on first trial ) *  p ( White on second trial )

                p ( X = 2 ) =  ( 2 / 5 ) * ( 3 / 4 )

                p ( X = 2 ) =  ( 3 / 10 )  

3) A red ball is drawn on the first draw and second draw and then a white ball is drawn on the third trial ( X = 3 ). The probability of drawing a red ball first would be ( 2 / 5 ). Then we are left with 4 balls in the urn, we again draw a red ball:

   p ( Red on second trial ) = ( Number of red balls ) / ( number of balls left )

   p ( Red on second trial ) = ( 1 ) / ( 4 )    

 

- Then draw a white ball from a total of 3 balls left in the urn ( remember without replacement ).                  

   p ( White on 3rd trial ) = ( Number of white balls ) / ( number of balls left )

   p ( White on 3rd trial ) = ( 3 ) / ( 3 ) = 1

- Then to draw red on first two trials and white ball on third trial we can express:

                p ( X = 3 ) =  p ( Red on 1st trial )*p ( Red on 2nd trial )*p ( White on 3rd trial )

                p ( X = 3 ) =  ( 2 / 5 ) * ( 1 / 4 ) * 1

                p ( X = 3 ) =  ( 1 / 10 )  

- The probability distribution of X is as follows:

    X          1                  2                      3

p ( X )      0.6               0.3                  0.1

- To verify the above the distribution. We will sum all the probabilities for all outcomes ( X = 1 , 2 , 3 ) must be equal to 1.

          ∑ p ( Xi ) = 0.6 + 0.3 + 0.1

                         = 1 ( proven it is indeed a pmf )

- The expected value E ( X ) of the distribution i.e the expected number of trials until we draw a white ball for the first time:

               E ( X ) = ∑ [ p ( Xi ) * Xi  ]

               E ( X ) = ( 1 ) * ( 0.6 ) + ( 2 ) * ( 0.3 ) + ( 3 ) * ( 0.1 )

               E ( X ) = 0.6 + 0.6 + 0.3

               E ( X ) = 1.5 trials until first white ball is drawn.

You might be interested in
1. Supposed that a population consists of the values 1.2.3.4.5.6.7.8, 9, and 10. Construct
irina [24]

Answer:

B

Step-by-step explanation:

Just pick B bro it isn't even that hard lol

8 0
3 years ago
When planning a date night, you have a choice of 2 types of restaurants: pizza (P) or barbeque (B); a choice of 3 types of movie
enot [183]

Answer:

S = \{PRC, PRI,PAC,PAI,PDC,PDI,BRC, BRI,BAC,BAI,BDC,BDI\}

Step-by-step explanation:

Given

Restaurant = \{P,B\}

Movies = \{R,A,D\}

Post-movie = \{C,I\}

Required

List out the sample space

To do this, we simply pick 1 item in each category, without repetition.

So, we have:

S = \{PRC, PRI,PAC,PAI,PDC,PDI,BRC, BRI,BAC,BAI,BDC,BDI\}

4 0
3 years ago
Pls help somebody how much does a can of coconut milk holds if 8cm in diameter and 12cm in height
dangina [55]
96ml (base times height | 8 times 12)
6 0
3 years ago
Find the slope of the line.
Archy [21]

Answer:

\displaystyle m=0.8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  1. Slope Formula: \displaystyle m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (4, 1.2)

Point (10, 6)

<u>Step 2: Find slope </u><em><u>m</u></em>

Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>

  1. Substitute [SF]:                    \displaystyle m=\frac{6-1.2}{10-4}
  2. Subtract:                              \displaystyle m=\frac{4.8}{6}
  3. Divide:                                 \displaystyle m=0.8
7 0
3 years ago
Read 2 more answers
If 2 over 5 tons of concrete covers 5 over 6 of a wall, how many tons of concrete are required to cover the entire wall?
Dominik [7]

Answer:

A. 12.25 tons

Step-by-step explanation:

We will let x represent the amount required to cover the entire wall.

We can divided 2/5 by 5/6 to solve for x

2/5 divided by 5/6=x

When you divide by a fraction, you can always multiply by the reciprocal (flipped number).

Our new equation is:

2/5·6/5=12/25

8 0
2 years ago
Other questions:
  • Find the missing side length, and enter your answer in the box below. If
    6·1 answer
  • What is the answer to<br> -12(-2-4x)
    12·2 answers
  • What is the value of 8x + 2x when x = 6?
    9·2 answers
  • The math club needs to raise more than $552. $.50 for a trip to state competition. The club has raise 12% of the funds which is
    13·1 answer
  • Given g(x) = -3x + 3, find g(-2).<br> Answer:<br> Submit Answer<br> Privacy Polic
    5·1 answer
  • coach Kent brings 3 quarts of sports drink to soccer practice he gives the same amount to each of his 16 players how many ounces
    11·2 answers
  • What is the percent for .3?
    12·2 answers
  • I Need help with this question please
    12·2 answers
  • Write the following number beds from one to number of the place value chart 5×100+8×1+2×1/10+3×1/100+1×1/1000 equals what number
    15·1 answer
  • What is the conjugate of 5+\sqrt{7}
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!