A soft drinks factory produces 1400 bottles a day. The factory tested a sample of 400 units and found that six were defective. By calculating the experimental probability that a bottle is defective, work out how many defective bottles would be expected in a day.
We’re told in the question that the factory tested a sample of 400 bottles and that six were defective. Six out of 400 can be written as a fraction six over 400. As the factory produces 1400 bottles in a day, we need to calculate six four hundredths of 1400. The word of in mathematics means multiply or times. We need to multiply six over 400 by 1400. The fraction six over 400 simplifies to three over 200 as both the numerator and denominator are divisible by two. Before multiplying three over 200 by 1400, we can cancel further. Both 200 and 1400 are divisible by 200. 200 divided by 200 is one, and 1400 divided by 200 is seven. This leaves us with the calculation three multiplied by seven, which is equal to 21.
We can, therefore, conclude that we would expect 21 of the bottles to be defective each day. An alternative method would be to use the fact that six out of 400 bottles were defective and then scale up and down. Dividing both numbers by two means that we would expect three out of 200 bottles to be defective. Multiplying both of these numbers by seven results in 21 out of 1400 bottles expected to be defective. This gives us the same answer as our first method.