Good Essay On Methods Analysis For Business Operations

An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the probability of:

- Drawing three yellow chips:
First, the chance will be 3/10. (3 yellow + 7 blues). After the first chip taken, it will be replenished, and again the second will be 3/10 again, and another is 3/10.

Replenishment makes this an independent probability,

thus P(ABC) = P(A)P(B)P(C) (Grinstead and Snell, 1998; George, 2004).
=3/10 x 3/10 x 3/10 = 0.027 = 2.7%
- Drawing a blue chip on the first draw and a yellow chip on the second draw.
Another independent probability. Replenishment makes the urn returns to the initial condition, even with 100 draws or more. Thus, the draw number n will be the same as the first draw, and it makes it an independent probability.
Drawing yellow or blue in the first run will never affect the rest of the draws. And this implies on all of the other questions.
=7/10 x 3/10 = 21/10 = 21%
- Drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw.

Since it is independent, result in the first draw does not need to be considered.

Chance for blue chip is 7/10 = 70%.
- Drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.

Since it is independent, result in the first draw does not need to be considered.

Chance for yellow chip is 3/10 = 30%.
- Drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw.
Similar to d, Chance for yellow chip is 3/10 = 30%.

References

George, G. (2004). 88.76 Testing for the independence of three events. The Mathematical Gazette, 568-568.
Grinstead, C. M., & Snell, J. L. (1998). Introduction to probability. American Mathematical Soc..