關於Probability的簡單Maths.問題

Tieria

2009-10-04 7:53 am

1. A group of students take turns to draw a card at random from a pack of 52 playing cards without replacement. The first student who draws a face card wins the game. George is the second one who draws a card. Find the probability that he wins.

The answer is 40 / 221.

2. Three letters are chosen at random from the word UNIVERSITY. Find the probability that all the letters chosen are vowels.

The answer is 1 / 30.

3. Five cards are marked with numbers 1, 4, 7, 10 and 13. Two cards are drawn at random from these cards. Find the probability that at least one of the cards is marked with an even number.

The answer is 7 / 10.

※請列明清楚計算步驟※

回答 (1)

Prof. Physics

2009-10-04 8:01 am

✔ 最佳答案

1. P(George to win)

= P(first student does not draw the face card) X P(George draws a face card)

= (1 - 12/52) X (12/51)

= 40/221

2. There are four vowels, and ten letters.

To choose 3 letters, the number of favourable outcome = 10C3

The probability = 4C3 / 10C3 = 1/30

3. P(at least one card is even)

= 1 - P(both are odd)

= 1 - 3/5 X 2/4

= 7/10

參考: Physics king

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