Answer:
The probability that X is 6 = 0.2508
Step-by-step explanation:
Probability of picking a red ball = 4 / 10 = 0.4
Probability of picking a white ball = 6 / 10 = 0.6
Let's first state that the last ball selected in this scenario will be red. This implies that we selected 6 white balls and 3 red balls in any manner before we selected the last red ball. So we need to find the probability of taking out 6 white balls and 3 red balls, and use permutation to account for the order they get drawn in:
Total Probability = Probability of 6 white balls * Probability of 3 red balls * number of ways this can happen
Probability of 6 white balls = 0.6 ^ 6
Probability of 3 red balls = 0.4 ^ 3
Number of ways this can happen (permutation with similar objects) = [tex]\frac{9!}{6!*3!}[/tex]
Number of ways this can happen = 84
Total probability = [tex]0.6^6 * 0.4^3 * 84[/tex]
Total probability = 0.2508
