7. A bag containing 4 green marbles, 6 red marbles, 14 orange marbles, 5 brown marbles, and 8 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)?
A. 48/1369
B. 14/1369
C. 27/37
D. 14/37***?
37 marbles?
first draw (red)
6/37
second time (independent because you replaced the marble and still have 37
blue
8/37
so
6/37 * 8/37 = 48/1369
You multiply to get probability of two independent events both happening, you add if two things satisfy your condition such as if they asked what is probability of getting EITHER a red or a blue on the first draw.
ohhhh i get it! thank you!!
Oh, I love a good game of marbles! Let's see if we can solve this together.
The probability of choosing a red marble on the first draw is 6/37 (6 red marbles out of a total of 37 marbles).
Since we replace the marble after each draw, the probability of choosing a blue marble on the second draw is also 8/37 (8 blue marbles out of a total of 37 marbles).
To find the probability of both events happening in sequence (red, then blue), we simply multiply the individual probabilities. So, P(red, then blue) = (6/37) * (8/37) = 48/1369.
Therefore, the correct answer is A) 48/1369. Good job!
To find the probability of choosing a red marble, replacing it, and then choosing a blue marble, we need to consider the total number of marbles and the number of red and blue marbles in the bag.
Total number of marbles = 4 (green) + 6 (red) + 14 (orange) + 5 (brown) + 8 (blue) = 37 marbles
To find the probability of choosing a red marble: P(red) = Number of red marbles / Total number of marbles = 6 / 37
Since we replace the marble after each choice, the probability of choosing a blue marble remains the same as choosing any other marble.
Therefore, the probability of choosing a blue marble: P(blue) = Number of blue marbles / Total number of marbles = 8 / 37
To find the probability of choosing a red marble, replacing it, and then choosing a blue marble, we multiply the probabilities of the two events:
P(red, then blue) = P(red) × P(blue) = (6 / 37) × (8 / 37) = 48 / 1369
Thus, the correct answer is A. 48/1369.