Box A contains 3 red and 2 blue marbles while Box B contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box A; if it turns up tails, a marble is chosen from Box B.
A. Find the probability that a red marble is chosen.
B. Referring to above information, suppose that the person who tosses the coin does not reveal whether it has turned up heads or tails (so that the box from which a marble was chosen is not revealed) but does reveal that a red marble was chosen. What is the probability that Box A was chosen (i.e., the coin turned up heads)?

Answer:

A. [tex]\frac{4}{10}[/tex]

B. [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given - Box A contains 3 red and 2 blue marbles while Box B contains 2

            red and 8 blue marbles. A fair coin is tossed. If the coin turns up

            heads, a marble is chosen from Box A; if it turns up tails, a marble

            is chosen from Box B.

To find -  A. Find the probability that a red marble is chosen.

              B. Referring to above information, suppose that the person who

                  tosses the coin does not reveal whether it has turned up

                  heads or tails (so that the box from which a marble was

                  chosen is not revealed) but does reveal that a red marble was

                  chosen. What is the probability that Box A was chosen (i.e.,

                  the coin turned up heads)?

Proof -

As given ,

Box A : 3 red marbles and 2 blue marbles.

Box B : 2 red marbles and 8 blue marbles.

a.)

As we have to find the probability that a red marble is chosen.

A red marble is chosen in two different ways - either it can be from Box A or Box be .

If Box A is chosen , then Probability of red ball is [tex]\frac{3}{5}[/tex]

If Box B is chosen , Then Probability of Red ball is [tex]\frac{2}{10} = \frac{1}{5}[/tex]

Now,

Probability of Box A is Chosen = [tex]\frac{1}{2}[/tex]

Probability of Box B is chosen = [tex]\frac{1}{2}[/tex]

∴ we get

Probability that a Red marble is chosen =  [tex]\frac{1}{2}[/tex]×[tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex]×[tex]\frac{1}{5}[/tex] = [tex]\frac{3}{10} + \frac{1}{10} = \frac{4}{10}[/tex] = 0.4

b.)

Now,

Probability that Box A is chosen given that Red marble is chosen is

P(Box A | Red marble ) = [tex]\frac{(\frac{3}{5})(\frac{1}{2}) }{(\frac{3}{5})(\frac{1}{2}) + (\frac{1}{5})(\frac{1}{2})} = \frac{\frac{3}{10} }{\frac{3}{10} + \frac{1}{10} } = \frac{\frac{3}{10} }{\frac{4}{10}}[/tex] = [tex]\frac{3}{4}[/tex]

How to covert feet into miles

Solve
9x^2 + 3x = 20

Write the equation of a line that has m=2 and passes through (-5, -6).

The probability of an event is
9
50
Describe the likelihood of the event.
o Certain
0 Likely
O Equally likely to happen or not happen
• Unlikely
o Impossible
Please help

George Smith own's George's Joint, a gas station and convenience store. George is trying to get a better understanding of his business and wants to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons of gasoline sold follows a normal distribution with a population standard deviation of 2.3 gallons. From his records, he randomly selects 60 sales and find the mean number of gallons sold is 8.6. What is the point estimate of the population mean

Simplify the following expression:
(i-3) +6i-3(8 - i)
A. 21+7
B. -27 +10;
C. 14 +6;
D. 8 +41

together, ben and kyle have 43 fishing lures. Kyle,(K), has 15 more lures than ben, (B). which statements are correct for this situation

which expression would be easier to simplify if you used the commutative property to change the order of the numbers​

Given a and b are numbers, and a + b = 180, which
statements also must be true?
a = 180 - 6
a - 180 = b
360 = 2a + 2b
a = 90 and b = 90

help me with this root problem....

Find the quotient.
(6x ^2 + 23x + 20) ÷ (5 + 2x)

a) 3x - 4
b) 3x + 4
c) 3x +19

There are 15 pieces of fruit in the fruit in a bowl and 6 of them are apples. What percentage of the pieces of the fruit in the bowl are apples

0.06%

0.4

6%

40%

Mrs. Hilt has 6 boxes of markers. Each box has 19 markers in it. If she sold each maker for $0.75, how much money would Mrs. Hilt earn?

could you help me pleas

two numbers are in the ratio 3 is to 5 what is the ratio between the squares
​

28cm, 62cm, 75cm is this a right triangle

Which of the following shapes is a prism? Select All that apply.
A. Shape 1: Circle
B. Shape 2: Cylinder
CShape 3: Rectangular Box
D. Shape 4: Cube
E. Shape 5: Pyramid
F. Shape 6: Cone

Can someone please help

Evaluate the following expressions: (2×3)2-52

Find the area of the rectangle below. Show your work​

There are 12 cupcakes. 3⁄4 of them have pink icing.
1⁄3 of the cupcakes with pink icing have sprinkles. How many of the cupcakes have pink icing and sprinkles?

please help me with this question

PLEASE HELP, will get brainliest​

pls help have a nice day

Help me please help help

Help! I’ll reward brainest its pretty easy

please help i dont get it​

if 25 worker need 3 days to build a house how long will 10 worker need

Explain how to solve 5x^2-3x=25 by completing the square. What are the solutions?

Scale factor from A to B is 4:5.
Help