Out of 1000 balls, 50 are red and the rest white. If 60 balls are picked at random, what is the probability of picking up (1) 3 red balls (2) not more than 3 red balls in the sample?
Answers
Step-by-step explanation:
10000___50 is the answer
Given,
Total number of balls = 1000
Number of red balls = 50
Number of white balls = 950
To find,
We have to find the probability of picking up (1) 3 red balls (2) not more than 3 red balls in the sample.
Solution,
The required probabilities are ⁵°C₃/¹°°°C₃ and ⁵°C₃/¹°°°C₃ + ⁵°C₂ * ⁹⁵°C₁/¹°°°C₃ + ⁵°C₁/¹°°°C₃.
We can simply find the required probabilities by using the concepts of combination.
Total number of cases of when picking 3 balls = ¹°°°C₃
Number of cases when 3 red balls are picked = ⁵°C₃
P( of picking 3 red balls) = ⁵°C₃/¹°°°C₃
(2) Number of cases of getting not more than 3 red balls in the sample = ⁵°C₃ + ⁵°C₂ * ⁹⁵°C₁ + ⁵°C₁
P( of picking not more than 3 red balls in the sample) = ⁵°C₃/¹°°°C₃ + ⁵°C₂ * ⁹⁵°C₁/¹°°°C₃ + ⁵°C₁/¹°°°C₃
Hence, the required probabilities are ⁵°C₃/¹°°°C₃ and ⁵°C₃/¹°°°C₃ + ⁵°C₂ * ⁹⁵°C₁/¹°°°C₃ + ⁵°C₁/¹°°°C₃.