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a bag contains the following fourteen marbles. deepak randomly chooses …

Question

a bag contains the following fourteen marbles.
deepak randomly chooses two marbles from the bag, one at a time, and replaces the marble after each choice. what is the probability he will choose one green marble and then one red marble? express the probabilities in fraction form.
p(green) =
p(red) =
p(green and red) =

Explanation:

Step1: Count total and green marbles

Total marbles: 14. Green marbles: 5 (count the green ones: first row green, second row green, third row green, fourth row green, and another green? Wait, let's list all: purple, green, red, green, blue, purple, blue, red, purple, green, green, blue, purple, and the last? Wait, the marbles are: purple (1), green (let's count: first row green, second row green, third row green, fourth row green, and another? Wait the image shows:

First row: purple, green, red, green (2 greens)

Second row: blue, purple, blue (wait no, second row: green (left), blue, purple, blue? Wait no, let's count again. Let's list each marble:

  1. purple
  1. green
  1. red
  1. green
  1. blue
  1. purple
  1. blue
  1. red
  1. purple
  1. green
  1. green
  1. blue
  1. purple
  1. green? Wait no, the fourth row: green, blue, purple? Wait the user's image: let's count green marbles:

Looking at the marbles:

  • Green: positions 2,4,10,11,14? Wait no, let's count again. Let's list all 14:
  1. purple
  1. green
  1. red
  1. green
  1. blue
  1. purple
  1. blue
  1. red
  1. purple
  1. green
  1. green
  1. blue
  1. purple
  1. green? Wait no, maybe I miscounted. Wait the problem says 14 marbles. Let's count green:

First row: green (2), second row: green (1), third row: green (2), fourth row: green (1)? Wait no, let's see the marbles:

  • Green marbles: let's count the number of green circles. From the image:

First row: green (1), green (2)

Second row: green (1) [the left one in second row? Wait no, second row: green (left), blue, purple, blue? No, the second row (middle) has green, blue, purple, blue? Wait no, the user's image:

The marbles are arranged as:

Top row: purple, green, red, green (2 greens)

Second row: green (left), blue, purple, blue (1 green)

Third row: purple, green, green (2 greens)

Fourth row: green, blue, purple (1 green)

Wait total green: 2 +1 +2 +1 =6? No, wait the problem says 14 marbles. Wait maybe I made a mistake. Wait the correct count: let's see the green marbles:

Looking at the image, the green marbles are:

  • First row: 2 (green, green)
  • Second row: 1 (green)
  • Third row: 2 (green, green)
  • Fourth row: 1 (green)

Total: 2+1+2+1=6? No, wait the user's problem says 14 marbles. Let's count all:

Purple: 4 (positions 1,6,9,13)

Red: 2 (positions 3,8)

Blue: 3 (positions 5,7,12)

Green: 14 -4 -2 -3 =5? Wait 4+2+3=9, 14-9=5. Ah, that's better. So purple: 4, red:2, blue:3, green:5. Yes, because 4+2+3+5=14. So green marbles: 5.

So P(green) = number of green / total = 5/14.

Step2: Count red marbles

Red marbles: 2 (positions 3,8). So P(red) = 2/14 = 1/7.

Step3: Probability of green then red (with replacement)

Since replacement, the events are independent. So P(green and red) = P(green) P(red) = (5/14) (2/14) = 10/196 = 5/98? Wait no, wait red marbles: 2? Wait earlier count: red marbles: positions 3 and 8, so 2. So P(red) = 2/14 = 1/7.

Wait let's recheck:

Total marbles:14.

Green:5, Red:2, Blue:3, Purple:4. 5+2+3+4=14. Correct.

So P(green) = 5/14.

P(red) = 2/14 = 1/7.

Then P(green and red) = (5/14) (2/14) = 10/196 = 5/98? Wait no, 52=10, 14*14=196, simplify 10/196 = 5/98. Wait but let's check again.

Wait red marbles: 2? Let's count the red circles: first row red, second row red? Wait the image: first row red (1), second row red (1)? Wait no, first row: red (1), second row: red (1)? Wait the marbles:

  • Red marbles: two (positions 3 and 8). So 2 red marbles. Correct.

So:

P(green) = 5/14.

P(red) = 2/14 = 1/7.

P(green and red) = (5/14) * (2/14) = 10/196 = 5/98. Wait but let's confirm…

Answer:

P(green) = $\frac{5}{14}$
P(red) = $\frac{1}{7}$
P(green and red) = $\frac{5}{98}$