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# probability

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Bowl A contains three red and two white chips, and bowl B contains four red and three white chips. A chip is drawn at random from bowl A and transferred to bowl B. Compute the probability of then drawing a red chip from bowl B.

Feb 17, 2020

$$P[\text{draw red from B}] = \\ P[\text{draw red from B|drew red from A}]P[\text{drew red from A}]+\\ P[\text{draw red from B|drew white from A}]P[\text{drew white from A}] = \\ \dfrac 5 8\dfrac 3 5+\dfrac 4 8 \dfrac 2 5 = \dfrac{23}{40}$$