A box contains 20 red balls and 40 green balls . Four balls are randomly selected from the box without replacement. What is the probability of selecting a red ball followed by a green ball and then another red ball followed by a green ball?

so you want the specific order, RGRG

prob(of that order)
= (20/60)(40/59)(19/58)(39/57)

= 260/5133 reduced to lowest terms
or
= appr .05065

To find the probability of selecting a red ball followed by a green ball and then another red ball followed by a green ball, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Step 1: Calculate the total number of ways to choose 4 balls out of a total of 60 balls.
Total number of ways = Combination (nCr) = 60 choose 4 = C(60, 4) = (60!)/(4!(60-4)!) = 487,635

Step 2: Calculate the number of favorable outcomes.
The probability of selecting a red ball is given by (20 red balls / 60 total balls) = 1/3.
After selecting a red ball, the number of green balls becomes 40-1 = 39.
The probability of selecting a green ball is given by (39 green balls / 59 remaining balls) = 39/59.
After selecting a green ball, the number of red balls becomes 20-1 = 19.
The probability of selecting a red ball is given by (19 red balls / 58 remaining balls) = 19/58.
After selecting a red ball, the number of green balls becomes 39-1 = 38.
The probability of selecting a green ball is given by (38 green balls / 57 remaining balls) = 38/57.

The number of favorable outcomes is (1/3) * (39/59) * (19/58) * (38/57).

Step 3: Calculate the probability of the favorable outcome.
Probability = Favorable outcomes / Total outcomes = [(1/3) * (39/59) * (19/58) * (38/57)] / 487,635

Therefore, the probability of selecting a red ball followed by a green ball and then another red ball followed by a green ball is [(1/3) * (39/59) * (19/58) * (38/57)] / 487,635.

To find the probability of this specific sequence of events, we need to consider the number of ways it can happen and divide it by the total number of possible outcomes.

Let's break it down step by step:

Step 1: Selecting a red ball
The number of red balls in the box is 20, and the total number of balls is 60 (20 red + 40 green). Therefore, the probability of selecting a red ball on the first draw without replacement is 20/60 or 1/3.

Step 2: Selecting a green ball
After the first ball is drawn, there are now 19 red balls and 40 green balls left in the box, making a total of 59 balls. Therefore, the probability of selecting a green ball on the second draw without replacement is 40/59.

Step 3: Selecting another red ball
Now that we have drawn a red ball and a green ball, there are 18 red balls and 39 green balls remaining in the box, making a total of 57 balls. The probability of selecting another red ball on the third draw without replacement is 18/57.

Step 4: Selecting another green ball
After drawing two red balls and one green ball, there are now 17 red balls and 38 green balls left in the box, making a total of 55 balls. Therefore, the probability of selecting a green ball on the fourth draw without replacement is 38/55.

Now, to find the probability of getting this specific sequence, we need to multiply the probabilities of each step together:

Probability = (1/3) * (40/59) * (18/57) * (38/55)

Calculating this expression will give us the desired probability.