Answer :
Answer:
3 / 95
Step-by-step explanation:
Solution:-
- The jar contains colored marbles that are distributed according to colors as follows:
Color Number of marbles
Red 8
Blue 6
Green 4
Yellow 2
Total 20
- We are to draw 2 marbles from the jar. After each draw the colored marble are not replaced. The probability of drawing any colored marble in each trial is dependent on the previous draw.
- We will investigate each draw separately. The probability to draw a green marble in the first draw.
p ( 1: Green ) = Favorable outcomes ( Green ) / Total number of marbles
- We have 4 Green marbles initially. So the number of favorable outcomes is 4.
The total number of balls in the jar are 20. Hence, the probability of drawing a green marble in first trial is:
p ( 1: Green ) = 4 / 20 = 1 / 5
- Since, the drawn green marble is not replaced the color distribution also changes for the next draw of a colored ball. The new colored marble distribution is:
Color Number of marbles
Red 8
Blue 6
Green 3
Yellow 2
Total 19
- We see that we are left with 3 green marbles in the jar and the total is now 19. Therefore, the probability of drawing green marble in the second draw given that we have drawn a green marble in first draw is:
p ( 2: green / 1: Green ) = Remaining green marbles / total marbles
p ( 2: green / 1: Green ) = 3 / 19
- The combined probability of drawing a green marble in first trial and again drawing a green marble in the second trial can be determined from conditional probability of dependent events.
p ( 1: Green & 2: Green ) = p ( 2: green / 1: Green )*p ( 1:Green )
p ( 1: Green & 2: Green ) = (1/5)*(3/19)
p ( 1: Green & 2: Green ) = 3 / 95 .... Answer