1. ## probability 3

Of the coffee makers sold in an appliance store, 6.0% have either a faulty switch or a defective cord, 2.4% have a faulty switch, and 0.3% have both defects. What percent of the coffee makers will have a defective cord?

2. Hello, arslan!

We are expected to know the formula:

. . $P(A \cup B) \;=\; P(A) + P(B) - P(A \cap B)$

Of the coffee makers sold in an appliance store,
6.0% have either a faulty switch or a defective cord,
2.4% have a faulty switch, and 0.3% have both defects.
What percent of the coffee makers will have a defective cord?
Let $S$ = faulty switch, $C$ = faulty cord.

We are told that: . $\begin{array}{ccc}P(S \cup C) &=& 0.06 \\ P(S) &=& 0.024 \\ P(S \cap C) &=& 0.03 \end{array}$

We have: . $P(S \cup C) \;=\;P(S) + P(C) - P(S \cap C)$

. . . . . . . . . . $0.06 \;\;\;= \;\;0.024 + P(C) \;\;-\;\; 0.03$

Therefore: . $P(C) \:=\:0.066$

3. Originally Posted by Soroban
Hello, arslan!

We are expected to know the formula:

. . $P(A \cup B) \;=\; P(A) + P(B) - P(A \cap B)$

Let $S$ = faulty switch, $C$ = faulty cord.

We are told that: . $\begin{array}{ccc}P(S \cup C) &=& 0.06 \\ P(S) &=& 0.024 \\ P(S \cap C) &=& 0.03 \end{array}$

We have: . $P(S \cup C) \;=\;P(S) + P(C) - P(S \cap C)$

. . . . . . . . . . $0.06 \;\;\;= \;\;0.024 + P(C) \;\;-\;\; 0.03$

Therefore: . $P(C) \:=\:0.066$
my answers are multiple choice and this answer is not one of the options?

4. Originally Posted by arslan
my answers are multiple choice and this answer is not one of the options?
Soroban made a simple careless mistake in converting one of the percentages into a decimal but his logic is perfectly sound. Your job is to find that simple error, fix it and then get the correct answer.

5. Originally Posted by Soroban
Hello, arslan!

We are expected to know the formula:

. . $P(A \cup B) \;=\; P(A) + P(B) - P(A \cap B)$

Let $S$ = faulty switch, $C$ = faulty cord.

We are told that: . $\begin{array}{ccc}P(S \cup C) &=& 0.06 \\ P(S) &=& 0.024 \\ P(S \cap C) &=& 0.03 \end{array}$

We have: . $P(S \cup C) \;=\;P(S) + P(C) - P(S \cap C)$

. . . . . . . . . . $0.06 \;\;\;= \;\;0.024 + P(C) \;\;-\;\; 0.03$

Therefore: . $P(C) \:=\:0.066$
Originally Posted by mr fantastic
Soroban made a simple careless mistake in converting one of the percentages into a decimal but his logic is perfectly sound. Your job is to find that simple error, fix it and then get the correct answer.
got it 3.9

6. Originally Posted by arslan
got it 3.9
3.9% is correct.