There are 6 runners in a marathon. A person may bet on the race by predicting th

Question

There are 6 runners in a marathon. A person may bet on the race by predicting the top three runners (without regard to order) or by predicting the 1st place winner. All runners have an equal chance of winning. Which bet is easier to win? A company produces 75% of its toothpaste overseas, 80% of its product from overseas contains fluoride, while only 30% of the domestic product has fluoride. Find the probability that a randomly picked tube of toothpaste was domestically produced given that it does NOT have fluoride.

Explanation / Answer

7. P( predicting top 3) = 1 / 6C3 = 1/20 = 0.05

P(predicting winner) = 1/6 = 0.1667

As, P(predicting winner) > P( predicting top 3)

The bet who predicting who comes 1st is easier.

8. Let D denote Domestic, O denote Overseas, NF denote no Fluoride

P(NF | D) = 1 - P(F|D) = 1 - 30% = 70%

P(NF | O) = 1 - P(F | O) = 1 - 80% = 20%

P(NF) = P(D)* P(NF | D) + P(O)* P(NF | O) = 25%*70% + 75%*20% = 32.50%

P(D | NF) = P(D)* P(NF | D) / P(NF) = 25%*70% / 32.50% = 11.61%

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