and 2 whAe urm contains 10 bails identical in every respect except color. There

Question

and 2 whAe urm contains 10 bails identical in every respect except color. There are 8 red balls ones. [20 points tree diagram that iBustrates this situation of drawing two balls with replacement and write the joint probabilities for the sample space b. What is the probability of drawing a red and a white ball (the order being irrelevant)? c. What is the probability of drawing two balls of the same color? d. Is drawing a red ball independent of drawing a white ball? Show proof using probability laws.

Explanation / Answer

B) P(drawing a red ball and a white ball) = 8C1 * 2C1/10C2 = 16/45 = 0.36

C) P(drawing two balls of the same colour) =8C2/10C2 + 2C2/10C2 = 28/45 + 1/45 = 29/45 = 0.64

D) P(drawing a red ball and a white ball) = 0

P(drawing a red ball) * P(drawing a white ball)

= 8C1/10C1 * 2C1/10C1

= 8/10 * 2/10 = 16/100 = 0.16

As P(drawing a red ball and a white ball) is not equal to P(drawing a red ball) * P(drawing a white ball) , SO they are not independent.

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