There are 10 colored balls in a box ( 5 red, 3 blue, 2 green ). What is the probability of picking out a red ball and then a blue ball ( If I do not replace the red ball

(5*3)/(10*9)=1/6

6. A bowl contains 10 red balls, 10 green balls and 10 white balls.

a. What is the probability of drawing 2 white balls with replacement?
b. What is the probability of drawing 2 white balls without replacement?

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a. Probability of drawing a white ball is 10(number of white balls)/ 30 (total number of balls) since the balls are replaced, the probability remains the same for the second ball, that is 10/30. To determine probability of drawing balls with replacement is found by multiplying both probabilities (10/30)*(10/30)

b. Probability of drawing without replacement is slightly different from with replacement. The first white ball is still 10/30 but the second will be the number of remaining white balls (9) divided by the remaining number of total balls (29). To determine probability, multiply the probabilities of each individual event. Thus, (10/30)*(9/29)

Well, let me crunch the numbers and find out for you! To calculate the probability, we first need to determine the total number of balls in the box. In this case, we have 10 balls.

Now, let's look at the probability of picking a red ball first. Out of the 10 balls, there are 5 red ones. So, the probability of picking a red ball is 5/10, which simplifies to 1/2.

Since you do not replace the red ball back into the box, there are now 9 balls remaining. Out of these 9 balls, there are 3 blue ones. Therefore, the probability of picking a blue ball after the red is 3/9, which simplifies to 1/3.

To find the overall probability, we multiply the probabilities of each event together.

So, the probability of picking a red ball and then a blue ball is (1/2) x (1/3) = 1/6.

There you have it! The probability of picking out a red ball and then a blue ball without replacing the red ball is 1/6.

To find the probability of picking out a red ball and then a blue ball without replacement, we need to consider the total number of outcomes and the desired outcomes.

Step 1: Find the total number of outcomes.
There are a total of 10 balls in the box. When we pick the first ball, there are 10 possible outcomes.

Step 2: Find the number of desired outcomes for picking a red ball.
There are 5 red balls in the box. When we pick the first ball, there are 5 desired outcomes of picking a red ball.

Step 3: Find the number of desired outcomes for picking a blue ball.
After picking the red ball, there are a total of 9 balls left in the box. 3 of these remaining balls are blue, so there are 3 desired outcomes of picking a blue ball.

Step 4: Multiply the probabilities of picking a red ball and then a blue ball.
The probability of picking a red ball is 5/10 (since there are 5 red balls out of a total of 10 balls).
The probability of picking a blue ball after picking a red ball is 3/9 (since there are 3 blue balls out of a remaining 9 balls).
To find the overall probability, multiply the two probabilities: (5/10) * (3/9) = 15/90 = 1/6.

Therefore, the probability of picking out a red ball and then a blue ball without replacement is 1/6.

red ball = 5/10, blue ball = 3/9

The probability of all events occurring is found by multiplying the probabilities of the individual events.