Problem

A box contains 6 red balls, 4 green balls, and 2 blue balls. You pull 2 balls from the box (one at a time) WITHOUT replacement. Find the probability of the following: P(Red on 1st ball AND Red on 2nd ball)

Solution

Step 1 :The box contains 6 red balls, 4 green balls, and 2 blue balls. We are to pull 2 balls from the box one at a time without replacement.

Step 2 :We are to find the probability of drawing a red ball on the first draw and a red ball on the second draw.

Step 3 :The probability of drawing a red ball on the first draw is the number of red balls divided by the total number of balls. This gives us \(\frac{6}{12} = 0.5\).

Step 4 :After drawing one red ball, the number of red balls reduces to 5 and the total number of balls reduces to 11. The probability of drawing another red ball is the number of remaining red balls divided by the remaining total number of balls. This gives us \(\frac{5}{11} = 0.45454545454545453\).

Step 5 :The probability of both events happening is the product of the probabilities of each event. This gives us \(0.5 * 0.45454545454545453 = 0.22727272727272727\).

Step 6 :Final Answer: The probability of drawing a red ball on the first draw and a red ball on the second draw is \(\boxed{0.227}\).

From Solvely APP
Source: https://solvelyapp.com/problems/18815/

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