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# [數學]機會率問題

Suppose that a bag contains 10 coins: 4 are fair, 3 are biased with probability of heads 1/3,

and 3 have heads on both sides. A coin is chosen at random from the bag and is then tossed.

(1) Find the probability that a tail is observed;

(2) Given that a tail is observed, find the probability that the chosen coin was a fair one.

### 1 Answer

- ☂雨後晴空☀Lv 710 years agoFavorite Answer
1)P(a tail is observed)= P(The chosen dice is fair and get tail) + P(The chosen dice is probability of heads 1/3 and get tail)= (4/10)(1/2) + (3/10)(1 - 1/3)= 2/5

2)P(Given that a tail is observed that the chosen coin was a fair one)= P(The chosen dice is fair and get tail) / P(a tail is observed) = (4/10)(1/2) / (2/5)= 1/2