Probability

從一副52張的撲克牌中隨機抽出一張牌和投擲一枚勻稱骰子一次。求抽出一張黑桃和擲得點數是奇數的概率。A card is randomly drawn from a pack of 52 playing cards and a fair dice is thrown once. Find the probability that the card drawn is a spade and the dice shows an odd number.

•  $\frac{1}{13}\times\frac{1}{3}=\frac{1}{39}$  
  

•  $\frac{1}{4}\times\frac{1}{2}=\frac{1}{8}$  
  

•  $\frac{1}{13}\times\frac{1}{2}=\frac{1}{26}$  
  

•  $\frac{1}{4}\times\frac{1}{3}=\frac{1}{12}$  
  

陳家成員有4男2女，周家成員有1男3女。從每個家庭中隨機選出一名成員，求選出的兩個成員都是男性的概率。There are 4 males and 2 females in the Chan family. There are 1 male and 3 females in the Chow family. One person is randomly selected from each family. Find the probability that 2 males are selected.

• $\frac{5}{10}=\frac{1}{2}$

• $\frac{4}{6}+\frac{1}{4}=\frac{11}{12}$

• $\frac{5}{6}\times\frac{3}{4}=\frac{5}{8}$

• $\frac{4}{6}\times\frac{1}{4}=\frac{1}{6}$

某射擊遊戲中，建文未能射中目標的概率是0.4。假設他發射兩次。求他沒有射中目標的概率。In a shooting game, the probability that Alan will not hit a target is 0.4. Suppose he shoots twice. Find the probability that he will not hit the target.

• 0.4x0.4=0.16

• (1-0.4)x0.4=0.24

• (1-0.4)x(1-0.4)=0.36

• 0.4+0.4=0.8

某射擊遊戲中，建文未能射中目標的概率是0.4。假設他發射兩次。求他在第一次發射射中目標但在第二次發射射不中的概率。In a shooting game, the probability that Alan will not hit a target is 0.4. Suppose he shoots twice. Find the probability that he will hit the target in the 1st shoot but not in the 2nd shoot.

• (1-0.4)X0.4=0.24

• (1-0.4)X0.4+0.4X(1-0.4)=0.48

• 0.4X0.4=0.16

• 0.6X0.6=0.36

某射擊遊戲中，建文未能射中目標的概率是0.4。假設他發射兩次。求他至少射中目標一次的概率。In a shooting game, the probability that Alan will not hit a target is 0.4. Suppose he shoots twice. Find the probability that he will hit the target at least once.

• 1-0.4X0.4=0.84

• 0.4X0.6+0.6X0.4=0.48

• 1-0.6X0.6=0.64

• 0.6X0.4+0.6X0.6=0.6

某瓶子中有3粒橙味糖和6粒西瓜味糖。從該瓶中隨機先後抽出兩粒糖，而抽出第一粒後並不放回。求抽出2粒西瓜味糖的概率。There are 3 orange sweets and 6 melon sweets in a jar. Two sweets are randomly chosen from the jar one by one without replacement. Find the probability that two melon sweets are chosen.

• $\frac{6}{9}\times\frac{5}{8}=\frac{5}{12}$

• $\frac{6}{9}\times\frac{6}{9}=\frac{4}{9}$

• $\frac{3}{9}\times\frac{2}{8}=\frac{1}{12}$

• $\frac{6}{9}\times\frac{6}{8}=\frac{1}{2}$

袋子X中有1個黑球和2個藍球，袋子Y中有3個黃球和4個藍球。從袋子X中隨機抽出一個球放入袋子Y中，然後從袋子Y中隨機抽出一個球。求從袋子Y中抽出藍球的概率。Box X contains 1 black ball and 2 blue balls. Box Y contains 3 yellow balls and 4 blue balls. A ball is randomly drawn from bag X and put into bag Y. Then a ball is randomly drawn from bag Y. Find the probability that the ball drawn from bag Y is blue.

• $\frac{1}{3}\times\frac{4}{8}=\frac{1}{6}$

• $\frac{2}{3}\times\frac{5}{8}=\frac{5}{12}$

• $\frac{1}{3}\times\frac{4}{8}+\frac{2}{3}\times\frac{5}{8}=\frac{7}{12}$

• $\frac{2}{3}\times\frac{4}{7}=\frac{8}{21}$