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
expeople1 [14]
3 years ago
14

Suppose we have three urns, namely, A B and C. A has 3 black balls and 7 white balls. B has 7 black balls and 13 white balls. C

has 12 black balls and 8 white balls. We first choose one urn from A, B and C. Then we randomly pick up two balls from that urn without replacement. Let Ai, i 1,2,3 denote the event that the urn we choose is A, B and C respectively. Suppose P(A1): P(A2): P(A3) =1:2:2. Compute :
(a) The probability that the first ball is black.
(b) The probability that the first ball is black given that the second ball is white.
Mathematics
1 answer:
professor190 [17]3 years ago
8 0

Answer:

a. 11/25

b. 11/25

Step-by-step explanation:

We proceed as follows;

From the question, we have the following information;

Three urns A, B and C contains ( 3 black balls 7 white balls), (7 black balls and 13 white balls) and (12 black balls and 8 white balls) respectively.

Now,

Since events of choosing urn A, B and C are denoted by Ai , i=1, 2, 3

Then , P(A1 + P(A2) +P(A3) =1 ....(1)

And P(A1):P(A2):P(A3) = 1: 2: 2 (given) ....(2)

Let P(A1) = x, then using equation (2)

P(A2) = 2x and P(A3) = 2x

(from the ratio given in the question)

Substituting these values in equation (1), we get

x+ 2x + 2x =1

Or 5x =1

Or x =1/5

So, P(A1) =x =1/5 , ....(3)

P(A2) = 2x= 2/5 and ....(4)

P(A3) = 2x= 2/5 ...(5)

Also urns A, B and C has total balls = 10, 20 , 20 respectively.

Now, if we choose one urn and then pick up 2 balls randomly then;

(a) Probability that the first ball is black

=P(A1)×P(Back ball from urn A) +P(A2)×P(Black ball from urn B) + P(A3)×P(Black ball from urn C)

= (1/5)×(3/10) + (2/5)×(7/20) + (2/5)×(12/20)

= (3/50) + (7/50) + (12/50)

=22/50

=11/25

(b) The Probability that the first ball is black given that the second ball is white is same as the probability that first ball is black (11/25). This is because the event of picking of first ball is independent of the event of picking of second ball.

Although the event picking of the second ball is dependent on the event of picking the first ball.

Hence, probability that the first ball is black given that the second ball is white is 11/25

​​

You might be interested in
What's the slope of (-5, 10) and (-2, -2)?
3241004551 [841]

Answer:

slope: -4

equation: y = -4x – 10

4 0
3 years ago
Can someone help out? No BS please. ​
oksian1 [2.3K]

Answer:

Angle EHG

Step-by-step explanation:

If you want explanation tell me in comments

4 0
3 years ago
Read 2 more answers
The current temperature in Smalltown is 19 °F. This is 7 degrees less than twice the temperature that it was six hours ago. What
Anna007 [38]

Answer:

5 degrees F

Step-by-step explanation:

because 7 x 2= 14

19-14=5

7 0
3 years ago
The chart shows the high temperature each day in Fairbanks, Alaska during the month of February 2009. What was the median high t
Montano1993 [528]

Answer:

Depends on the data

Step-by-step explanation:

You need to arrange all of the data from the chart in numerical order.

Then figure out which number/numbers are in the middle of the data line.

If it was just one number that is the median. If two numbers were in the middle add them together then divide by two, that is your median.  

7 0
3 years ago
Read 2 more answers
26 is the product of Rita's score and 2
earnstyle [38]
If it’s division try 13 not rlly sure so don’t give me hate if it wrong
3 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the problem. Make sure your answer is in simplest form. 3/16 x 4/21 = ?
    6·1 answer
  • 5 friends will equally share the 3 jars of honey they got from their beehive.
    9·1 answer
  • How is the total price including sales tax calculated
    7·1 answer
  • Calculate (-3 5/6) - 4 1/2
    7·1 answer
  • A quadradic polynomial has a degree of 2 true or false
    10·1 answer
  • Help asap! This is due in three hours! Casey wants to buy a gym membership. One gym has a $156 joining fee and costs $29 per mon
    5·1 answer
  • Jena bought $8 shirt and paid $8.48 with a sales tax. what is the percent of sales tax
    15·2 answers
  • Owen and Bella shared a granola bar. Bella ate 14 of the granola bar. Owen ate 13 of the bar. How much of the granola bar did Ow
    15·1 answer
  • I need to know the answer to this is radical form
    14·1 answer
  • How much times longer is Jupiter’s orbit than earth’s orbit?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!