問 1
1 点For two events \(A\) and \(B\), it is given that \(P(A) = 0.3\), \(P(B) = 0.5\), and \(P(A | B) = 0.4\). Calculate the conditional probability \(P(B | A)\).
Oxford AQA International A-level · Mathematics (9660)
Further probability：練習問題
その場で採点される選択問題 5 問と、解説つきの記述問題 5 問。すべて「Further probability」からの出題です。
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問 2
1 点The conditional probabilities for event \(A\) given event \(B\) and its complement \(B'\) are \(P(A | B) = 0.7\) and \(P(A | B') = 0.4\). If \(P(B) = 0.3\), calculate the value of \(P(B | A)\).
問 3
1 点Two events \(A\) and \(B\) are mutually exclusive. Given that \(P(A) = 0.25\) and \(P(B) = 0.45\), find the value of \(P(A' \cap B')\).
問 4
1 点For two events \(A\) and \(B\), it is given that \(P(A | B) = 0.5\), \(P(B | A) = 0.4\), and \(P(A \cap B) = 0.2\). Calculate \(P(A' \cap B')\).
問 5
1 点Events \(A\) and \(B\) are independent such that \(P(A) = 0.6\) and \(P(B) = 0.5\). Calculate \(P(A \cup B)\).
問 6
3 点Events \(A\) and \(B\) are independent such that \(P(A) = 0.4\) and \(P(A \cup B) = 0.7\). Calculate the probability \(P(B)\).
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 7
6 点Given that \(P(A) = 0.6\), \(P(B) = 0.5\), and \(P(A | B) = 0.8\), find the conditional probability \(P(B | A')\).
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 8
5 点Three events \(A\), \(B\), and \(C\) are defined. Events \(A\) and \(B\) are mutually exclusive with \(P(A) = 0.3\) and \(P(B) = 0.4\). If event \(C\) is independent of the event \((A \cup B)\) and \(P(C) = 0.5\), find \(P((A \cup B) \cap C)\).
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 9
4 点For two events \(A\) and \(B\), it is given that \(P(A) = 0.35\), \(P(B) = 0.45\), and \(P(A \cup B) = 0.6\).
(a) Calculate \(P(A \cap B)\).
(b) Find the conditional probability \(P(A | B)\).
(c) Determine, with a reason, whether events \(A\) and \(B\) are independent.
まず自分で答えを書いてから、解説と照らし合わせましょう。
問 10
6 点In a factory, machine A produces 60% of the total output and machine B produces the remaining 40%. The probability of a defective component being produced by machine A is 0.02, while the probability for machine B is 0.05.
(a) A component is selected at random from the total output. Find the probability that it is defective.
(b) Given that a randomly selected component is found to be defective, find the probability that it was produced by machine A.
(c) Two components are selected at random. Find the probability that exactly one is defective.
まず自分で答えを書いてから、解説と照らし合わせましょう。
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