Final answer:
The probability of selecting a red ball and then a yellow ball from a bag containing 6 balls (4 red, 2 yellow) without replacement is 4/15.
Step-by-step explanation:
Calculating the Probability of Selecting a Red Ball Then a Yellow Ball
The problem describes a scenario where there are 6 balls in a bag: 4 red and 2 yellow. We are interested in finding the probability that a student selects a red ball first, and then a yellow ball, without replacing the first ball. To solve this, we calculate the probability step by step.
The probability of selecting a red ball first is the number of red balls divided by the total number of balls:
P(Red first) = 4 red balls / 6 total balls = 2/3
Since the red ball is not replaced, there are now only 5 balls left in the bag: 3 red and 2 yellow. Hence, the probability of then selecting a yellow ball is:
P(Yellow second | Red first) = 2 yellow balls / 5 remaining balls = 2/5
To find the total probability of both events occurring in succession (selecting a red ball then a yellow one), we multiply the individual probabilities:
Total probability = P(Red first) × P(Yellow second | Red first) = (2/3) × (2/5) = 4/15
The probability of selecting a red ball first and then a yellow ball without replacement is 4/15.