So, the task is: There are two companies, A and B. The first company A uses the technology which consists of two operations in a row to get a product. The probability of getting a defect product from first operation is 0.4 and from the second one 0.5. The company B uses another technology which consists of three operations. The probability of getting a defect product from first operation is 0.1,from the second 0.2 and from the third 0.3. In company A there are 90% of first class products among working products (which are not defect) and in company B there are 70% of first class products among working products. Which technology (A's or B's) has a bigger probability of giving a first class product? This task sounds confusing to me and I'm not sure where to start...
This is really simple. For company A, you want the probability that:
- First step goes well ($P=1-0.4=0.6$) AND
- Second step goes well ($P=1-0.5=0.5$) AND
- You win the raffle? ($P=0.9$)
Whenever you have and, you multiply. So the probability of having a 1st class product is the product of all of these:
$$P_A= 0.6 \times 0.5 \times 0.9=0.27=27 \%$$
Same exact thing for B, except of course the probabilities are different (and there's another step). We want the probability of:
- First step goes well ($P=1-0.1=0.9$) AND
- Second step goes well ($P=1-0.2=0.8$) AND
- Third step goes well ($P=1-0.3=0.7$) AND
- It's the chose one ($P=0.7$)
Again, multiply them all:
$$P_B = 0.9 \times 0.8 \times 0.7 \times 0.7 =0.3528=35.28\%$$
Therefore, technology B has a higher probability of giving a 1st class product.