A bag contains three red marbles and seven blue marbles you pick a marble don’t replace it then pick another what is the probability of picking a red marble then a blue marble

Answer 1

To find the probability of picking a red marble first and then a blue marble, we can break it down into two separate events:

Event 1: Picking a red marble first
Since there are 3 red marbles and a total of 10 marbles in the bag, the probability of picking a red marble first is 3/10.

Event 2: Picking a blue marble second
After picking a red marble, there will be 9 marbles left in the bag, with 7 of them being blue. Therefore, the probability of picking a blue marble second is 7/9.

To find the overall probability of both events happening consecutively, we multiply the individual probabilities:
P(red then blue) = P(red) * P(blue|red)
P(red then blue) = (3/10) * (7/9)
P(red then blue) = 21/90
P(red then blue) = 7/30

Therefore, the probability of picking a red marble first and then a blue marble is 7/30 or approximately 0.2333 (rounded to four decimal places).