Problem

Pieces of wood cladding are produced by a timber merchant. There are three types of fault, $A$, $B$ and $C$, that can appear in each piece of wood cladding.

The Venn diagram shows the probabilities of a piece of wood cladding having the various types of fault.

A piece of wood cladding is chosen at random.

(a) Find the probability that the piece of wood cladding has more than one type of fault.

Fault types $A$ and $C$ occur independently.

(b) Find the probability that the piece of wood cladding has no faults.

Given that the piece of wood cladding has fault $A$,

(c) find the probability that it also has fault $B$ but not fault $C$.

Two pieces of the wood cladding are selected at random.

(d) Find the probability that both have exactly 2 types of fault.

中文翻译

一家木材商生产木质覆板。每块覆板可能出现 $A$、$B$、$C$ 三类缺陷，文氏图给出了出现各类缺陷的概率。随机选取一块覆板。

(a) 求该覆板具有多于一种缺陷的概率。

已知缺陷 $A$ 与 $C$ 相互独立。

(b) 求该覆板没有任何缺陷的概率。

已知该覆板具有缺陷 $A$。

(c) 求它同时具有缺陷 $B$、但没有缺陷 $C$ 的概率。

随机选取两块覆板。

(d) 求两块覆板都恰有两类缺陷的概率。