Goal: Pick a red ball. Jar 1 = 50 red balls and 50 black balls Jar 2 = 90 balls

Question

Goal: Pick a red ball.

Jar 1 = 50 red balls and 50 black balls

Jar 2 = 90 balls of one color (red or black) and 10 balls of theother color

Question: Which jar would you pick from...AKA which jar setup gives you a higher probability of picking a red ball?

Attempt: I really have no idea but I thought since there are twocolors (red and black) there are two ways Jar 2 can be set up andthus a 50/50 chance that it is in your favor (90 red balls) so bestcase scenario is (1/2)*(9/10) = 9/20. For Jar 1 theprobability for picking a red ball is 1/2 so it is more favorablebut I really don't know what to do about Jar 2.

Please help - Thank You

Explanation / Answer

The probability that you draw a red ball from the first Jaris: P(Red|First Jar) = 1/2 The probability that you draw a red ball from the second Jaris: P(Get a Red|Red Gets 90) = 1/2 * 9/10 = 9/20 + P(Get a Red|Blue Gets 90) = 1/2 * 1/10 = 1/20 (You candraw a red even if blue gets 9/10 balls)    Therefore, P(Red|Jar 2) = 9/20 + 1/20 = 1/2 So the probability is the same for both Jars.

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