topic tree diagram. a box contain 6red and 4blue,5white balls.there balls are the bag one after the other without replacement find the prob of obtaining
1 first the same colour 2 first blue 2nd red,than white. 3. 1st red. 4different colours
To solve these probability questions, we can create a tree diagram. A tree diagram is a graphical way to represent the different outcomes of an experiment or event.
1. Probability of obtaining the same color as the first ball:
For the first question, we need to find the probability of getting the same color for both balls. Start by drawing a tree diagram with two branches at the first level: one for a red ball and one for a blue ball.
On the red branch, there are 6 red balls left, and on the blue branch, there are 4 blue balls left. Calculate the probability of choosing a red ball on the first draw: 6/15. The probability of choosing a red ball on the second draw will depend on what happened on the first draw. If a red ball is chosen first, there will be 5 red balls left out of 14. If a blue ball is chosen first, there will still be 6 red balls left out of 14. Calculate the probabilities for each scenario and then add them up:
P(2 red balls) = (6/15) * (5/14)
P(2 blue balls) = (4/15) * (3/14)
P(same color) = P(2 red balls) + P(2 blue balls)
2. Probability of first blue, second red, and third white:
For the second question, we need to find the probability of getting a blue ball on the first draw, followed by a red ball on the second draw, and then a white ball on the third draw.
Extend the tree diagram by adding a third level for the white balls. Calculate the probabilities for each scenario:
P(blue, red, white) = P(blue) * P(red) * P(white)
P(blue) = 4/15
P(red) = 6/14 (since one ball has already been drawn and not replaced)
P(white) = 5/13 (since two balls have already been drawn and not replaced)
3. Probability of obtaining the first red ball:
For the third question, calculate the probability of drawing a red ball first:
P(red) = 6/15
4. Probability of obtaining four different colors:
For the fourth question, find the probability of selecting balls of all different colors. Since there are three colors to choose from (red, blue, and white), we will need three branches on the first level of the tree diagram. Calculate the probabilities for each scenario:
P(different colors) = P(red, blue, white) + P(blue, red, white) + P(white, blue, red)
Remember to adjust the probabilities for each level based on the number of balls remaining after each draw.
This is how you can use a tree diagram to find the probabilities for the given scenarios.