two balls are drawn in succession,without replacement, from the box containing 3 red and 2 white balls, what is the probability of drawing a white on the second draw?
Assuming a red ball is chosen on first draw, P(w) = 2/4
Assuming a white ball is chosen on first draw, P(w) = 1/4
Either-or probabilities are found by adding the individual probabilities.
To find the probability of drawing a white ball on the second draw, we need to consider the possible outcomes.
Let's break it down step-by-step:
Step 1: Determine the total number of balls in the box.
In this case, we have a box containing 3 red balls and 2 white balls, so the total number of balls is 3 + 2 = 5.
Step 2: Determine the total number of ways to choose 2 balls from the box without replacement.
This can be calculated using the concept of combinations. The total number of ways to choose 2 balls from 5 is calculated as 5C2 = 5! / (2! * (5-2)!) = 10.
Step 3: Calculate the total number of ways to draw a white ball on the second draw.
Since we are drawing without replacement, after drawing the first ball, the box has one less ball. So, on the second draw, there are 4 balls left in the box. The number of ways to draw a white ball on the second draw is equal to the number of white balls left in the box, which is 2.
Step 4: Calculate the probability of drawing a white ball on the second draw.
The probability is calculated by dividing the desired outcome (the total number of ways to draw a white ball on the second draw) by the total number of possible outcomes (the total number of ways to choose 2 balls from the box).
Probability = Number of ways to draw a white ball on the second draw / Total number of ways to choose 2 balls from the box
Probability = 2 / 10
Probability = 1/5
So, the probability of drawing a white ball on the second draw is 1/5 or 0.2.