The manufacturer

The manufacturer found that 3% of the plates produced had a malfunction. Of the compliant, 75% are first and 25% second. What is the probability of producing first and second class plates?

Correct answer:

p₁ =  72.75 %
p₂ =  24.25 %

Step-by-step explanation:

$$\begin{gathered} q=1-3\mathrm{/}100={\displaystyle \frac{97}{100}}=0.97 \\ {k}_1=75\mathrm{\%}={\displaystyle \frac{75}{100}}=0.75 \\ {k}_2=25\mathrm{\%}={\displaystyle \frac{25}{100}}=0.25 \\ {p}_1=100\cdot q\cdot k_1=100\cdot 0.97\cdot 0.75=72.75\mathrm{\%} \end{gathered}$$

$p_2=100\cdot q\cdot k_2=100\cdot 0.97\cdot 0.25=24.25\mathrm{\%}$

Try another example

Related math problems and questions:

• Shooters
  In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.
• Sales off
  shoes cost x euros. First they are discounted by 50%, and then 25% of the new amount. Determine what percentage of the total cost is cheaper.
• Four numbers
  The first number is 50% second, the second number is 40% third, the third number is 20% of the fourth. The sum is 396. What are the numbers?
• Lathe
  95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
• Final exam
  There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
• Sum of three numbers
  The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
• Two math problems
  1) The sum of twice a number and -6 is nine more than the opposite of that number. Find the number. 2) A collection of 27 coins, all nickels, and dimes, is worth $2.10. How many of each coin are there? The dime, in United States usage, is a ten-cent coin.
• Lions
  If 8 lions is 40% how many would 75% be?
• Alcohol 2
  Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
• A number
  A number 5% greater than 75?
• Two shops
  In two different shops, the same skis had the same price. In the first, however, they first became more expensive by 20% and then cheaper by 5%. In the second, they were first cheaper by 5% and then more expensive by 30%, so after these adjustments in the
• 3 days
  Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day.
• Skis
  Skis, which cost € 800, became 25% more expensive before the season. After the season, they became cheaper again by 25%. How many euros did the skis cost after the discount?
• Two doctors
  Doctor A will determine the correct diagnosis with a probability of 93% and doctor B with a probability of 79%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.
• 3y inflation
  Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
• The cube
  The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8?
• Percent chaining
  Calculate 20% from 70% from 80 km