A bag contains 2 black balls, 4 yellow balls and 4 white balls. Event A is defined as drawing a white ball on the first draw and event B is defined as drawing a black ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form? A. B. C. D.

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JeanaShupp JeanaShupp · Answer 1 · 2021-03-16T01:59:53+01:00

Answer: [tex]P(B|A)=\dfrac{4}{9}[/tex]

Step-by-step explanation:

Given: A bag contains 2 black balls, 4 yellow balls and 4 white balls.

Event A is defined as drawing a white ball on the first draw.

Event B is defined as drawing a black ball on the second draw.

P(B|A) is expressed as the conditional probability of occurring B given that A.

i.e. it is the probability of happening B where A is already happended.

If a white ball is drawn at first, then the number of black ball(4) remains unchanged but the total number of balls (10) will become 9.

[tex]Probability=\dfrac{Number\ of \ favorable \ outcomes}{Total\ outcomes}[/tex]

Then, [tex]P(B|A)=\dfrac{4}{9}[/tex]