NationalHardProbability10–12

Machine $A$ makes $60\%$ of the pieces and $2\%$ of them are defective; machine $B$ makes the other $40\%$ and $5\%$ of those are defective. A defective piece is drawn. What is the probability that it came from $A$ ?

A máquina $A$ produz $60\%$ das peças e $2\%$ delas saem defeituosas; a máquina $B$ produz os restantes $40\%$ e $5\%$ dessas saem defeituosas. Retira-se uma peça defeituosa. Qual é a probabilidade de ter vindo de $A$ ?

Answer options

Solution

Step 1 of 3

1.The pieces that are defective and from $A$ are $0.6 \times 0.02 = 0.012$ of the total; from $B$ they are $0.4 \times 0.05 = 0.02$ .

Machine AAA makes 60%60\%60% of the pieces and 2%2\%2% of them are defective; machine BBB makes the other 40%40\%40% and 5%5\%5% of those are defective. A defective piece is drawn. What is the probability that it came from AAA?

Answer options

Machine $A$ makes $60\%$ of the pieces and $2\%$ of them are defective; machine $B$ makes the other $40\%$ and $5\%$ of those are defective. A defective piece is drawn. What is the probability that it came from $A$ ?