Question

probability qtn:
choose from 1st barrel : 5 out of 50 balls plus also then choose from a second barrel 2 out of 11 balls. Probability is = 50 X 49 X 48 X 47 X 46 X 11 X 10 = 27 billion but stated odds are 116 million......which is correct?

Answer 1

32953:

Task.

Choose from 1st barrel : 5 out of 50 balls plus also then choose from a second barrel 2 out of 11 balls. Probability is = 50 X 49 X 48 X 47 X 46 X 11 X 10 = 27 billion but stated odds are 116 million...which is correct?

Solution. Both are incorrect, probability is a number not greater than 1. Consider events: A={to choose 5 out of 50 balls from 1st barrel }, B={ to choose 2 out of 11 balls from second barrel }, C={ to choose 5 out of 50 balls from 1st barrel and then to choose 2 out of 11 balls from second barrel }. By classical definition of probability find the probability of event A and B: $p(A) = \frac{5}{50}, \ p(B) = \frac{2}{11}$. These events are successive and independent, and unknown probability is

$$p(C) = \frac{5}{50} * \frac{2}{11} = \frac{1}{55} \approx 0.018.$$