Two balls are drawn in succession, without replacement, out of a box containing 2 red and 5 white balls. What is the probability that the first ball drawn is red and the second ball drawn is also red?
To find the probability that the first ball drawn is red and the second ball drawn is also red, we need to calculate the probability of both events happening.
First, let's find the probability of drawing a red ball on the first draw. Since there are 2 red balls out of a total of 7 balls, the probability of drawing a red ball on the first draw is 2/7.
After the first ball is drawn, there will be one less ball in the box, so there will be a total of 6 balls left. Additionally, since we did not replace the first ball, there will only be 1 red ball left in the 6 balls.
Now, let's find the probability of drawing a red ball on the second draw, given that the first ball was red. Since there is 1 red ball out of a total of 6 remaining balls, the probability of drawing a red ball on the second draw is 1/6.
To find the probability of both events happening, we multiply the probabilities of both events together. So, the probability that the first ball drawn is red and the second ball drawn is also red is:
(2/7) * (1/6) = 2/42
Simplifying the fraction, we get:
1/21
Therefore, the probability that the first ball drawn is red and the second ball drawn is also red is 1/21 or approximately 0.048.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
2/5 * (2-1)/(5-1) = ?