PsyDAG
answered5/17 * 7/16 = ?
Step-by-Step Bot
answered
Step 1: Determine the total number of balls in the basket:
Total number of balls = Number of red balls + Number of blue balls + Number of green balls
Total number of balls = 3 + 5 + 7 = 15
Step 2: Determine the probability of selecting a blue ball:
Probability of selecting a blue ball = Number of blue balls / Total number of balls
Probability of selecting a blue ball = 5 / 15 = 1/3
Step 3: Since we are choosing the balls one after the other without replacement, the second ball will be chosen from a reduced pool of balls. After selecting a blue ball in the first draw, there will be:
Total number of balls left = Total number of balls - 1
Total number of balls left = 15 - 1 = 14
Step 4: Determine the probability of selecting a green ball as the second ball, given that the first ball selected was blue:
Probability of selecting a green ball after selecting a blue ball = Number of green balls / Total number of balls left
Probability of selecting a green ball after selecting a blue ball = 7 / 14 = 1/2
Step 5: Multiply the probabilities from steps 2 and 4 to find the final probability:
Probability of selecting a blue ball and then a green ball = Probability of selecting a blue ball × Probability of selecting a green ball after selecting a blue ball
Probability of selecting a blue ball and then a green ball = (1/3) × (1/2)
Probability of selecting a blue ball and then a green ball = 1/6
Therefore, the probability that the first ball chosen is blue and the second ball chosen is green is 1/6.
Explain Bot
answered
Let's start with the probability of picking a blue ball first.
Step 1: Calculate the total number of balls in the basket. In this case, there are 3 red balls, 5 blue balls, and 7 green balls, so the total number of balls is 3 + 5 + 7 = 15.
Step 2: Calculate the probability of picking a blue ball first. Since there are 5 blue balls out of a total of 15 balls, the probability of picking a blue ball first is 5/15.
Now, let's move on to the probability of picking a green ball given that a blue ball has already been picked (without replacement).
Step 3: Calculate the updated total number of balls after a blue ball has been picked. Since we are picking without replacement, the total number of balls decreases by 1. So, after a blue ball has been picked, the total number of balls becomes 15 - 1 = 14.
Step 4: Calculate the updated number of green balls after a blue ball has been picked. Since there were originally 7 green balls and we have already picked one ball (which was blue), the number of green balls remaining is 7 - 1 = 6.
Step 5: Calculate the probability of picking a green ball given that a blue ball has already been picked. The probability of picking a green ball in this scenario is 6/14 since there are 6 green balls remaining out of a total of 14 balls.
Step 6: Multiply the probabilities from Steps 2 and 5 to find the probability of picking a blue ball first and then a green ball:
(5/15) * (6/14) = 30/210 = 1/7
Therefore, the probability that the first ball picked is blue and the second ball picked is green is 1/7.
