A jar has 4 red marbles, 6 blue marbles, and and 5 green marbles. you select two marbles at random. one marble is drawn and not replaced. then a second marbel is drawn. what is the probability of selecting a red marble then another red mrble
The probability of selecting a red marble on the first draw is 4/15 (4 red marbles out of 15 total marbles in the jar).
Since the first marble is not replaced, there are now 14 marbles left in the jar. If we want to select another red marble, there are now only 3 red marbles left out of the remaining 14. So the probability of selecting a red marble on the second draw given that the first marble was red is 3/14.
To find the probability of both events happening (selecting a red marble followed by another red marble), we need to multiply the two probabilities:
(4/15) x (3/14) = 2/105
Therefore, the probability of selecting a red marble followed by another red marble is 2/105.
2/105 simplified
2/105 is already in its simplest form as the numerator 2 and the denominator 105 do not have any common factors other than 1.
To calculate the probability of selecting a red marble, and then another red marble without replacement, we need to follow these steps:
Step 1: Calculate the probability of selecting a red marble on the first draw.
Step 2: Calculate the probability of selecting a red marble on the second draw given that the first marble drawn was red.
Step 3: Multiply the probabilities from Step 1 and Step 2 to get the probability of both events happening.
Step 1: Probability of selecting a red marble on the first draw.
There are a total of 4 red marbles, 6 blue marbles, and 5 green marbles. So, the probability of selecting a red marble on the first draw is 4/15.
Step 2: Probability of selecting a red marble on the second draw given that the first marble drawn was red.
After removing one red marble from the jar, there are now 3 red marbles left. Since we do not replace the marble after drawing, the total number of marbles in the jar decreases to 14. So, the probability of selecting a red marble on the second draw given that the first marble was red is 3/14.
Step 3: Multiply the probabilities from Step 1 and Step 2.
To find the probability of both events happening (selecting a red marble on the first draw and then selecting another red marble on the second draw), we multiply the probabilities from Step 1 and Step 2:
(4/15) * (3/14) = 12/210 = 2/35
Therefore, the probability of selecting a red marble on the first draw and then selecting another red marble on the second draw is 2/35 or approximately 0.057 (rounded to three decimal places).