a box contains seven red marbles, five green marbles & eight blue marble. a marble is drawn at random & is replaced. a second marble is then drawn from ther jar. find the probabilty that the first marble is red & second is green
prob(red, then green)
= (7/20)(5/20)
= 35/400
= 7/80
To find the probability that the first marble drawn is red and the second marble is green, you need to first determine the total number of marbles in the box and the number of red and green marbles specifically.
Given information:
- Total number of marbles = 7 (red) + 5 (green) + 8 (blue) = 20 marbles
- Number of red marbles = 7
- Number of green marbles = 5
Since the marbles are replaced after each draw, the probability of each draw remains the same.
Step-by-step calculation:
1. Find the probability of drawing a red marble on the first draw:
P(red on first draw) = Number of red marbles / Total number of marbles
= 7 / 20
2. Find the probability of drawing a green marble on the second draw:
P(green on second draw) = Number of green marbles / Total number of marbles
= 5 / 20
3. Find the probability of both events happening (red first, green second):
P(red first, green second) = P(red on first draw) * P(green on second draw)
= (7 / 20) * (5 / 20)
= 35 / 400
4. Simplify the fraction (if needed) to get the final probability:
P(red first, green second) = 7 / 80
Therefore, the probability that the first marble drawn is red and the second marble is green is 7/80.