A bag contains 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)?
48/1369
14/1369
27/37
14/37
The probability of choosing a red marble on the first draw is 6/37. Since the marble is replaced, the probability of choosing a blue marble on the second draw is 8/37. Therefore, the probability of P(red, then blue) is:
P(red, then blue) = P(red) * P(blue) = (6/37) * (8/37) = 48/1369
So the answer is 48/1369.
Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 14 red balls. Urn II contains 4 green balls and 11 red balls. If a ball is drawn from each urn, what is P(red and red)?
1/9
25/39
79/60
77/180
The probability of drawing a red ball from Urn I is 14/(10+14) = 7/12. The probability of drawing a red ball from Urn II is 11/(4+11) = 11/15.
To find the probability of both events happening together, we multiply the probabilities:
P(red and red) = P(red from Urn I) * P(red from Urn II)
P(red and red) = (7/12) * (11/15)
P(red and red) = 77/180
Therefore, the probability of drawing a red ball from both urns is 77/180.
Hence, the answer is 77/180.
To find the probability of selecting a red marble, replacing it, and then selecting a blue marble, we need to consider the number of red marbles and the number of blue marbles in the bag.
There are a total of 4 + 6 + 14 + 5 + 8 = 37 marbles in the bag.
The probability of selecting a red marble on the first draw is 6/37, since there are 6 red marbles out of 37 total marbles.
Since the first marble is replaced, the number of red marbles remains the same at 6. Similarly, the number of total marbles is still 37.
The probability of selecting a blue marble on the second draw is 8/37, since there are 8 blue marbles out of 37 total marbles.
To find the probability of both events occurring, we multiply the probabilities.
Therefore, the probability of selecting a red marble, replacing it, and then selecting a blue marble is (6/37) * (8/37) = 48/1369, which is approximately 0.035177.
So, the correct answer is 48/1369.