Five workers are supposed to paste expiration date on each can.A,who paste 30% of the cans,fail to paste the expiration date once in every 300cans.B,who paste 15%,fail to paste the expiration date once in every 250cans.C,who paste 35% ,fail to paste the expiration date once in every 100 cans.D,who paste 7%,fail to paste the expiration date once in every 150cans and E,who paste 13%,fail to paste the expitation date once in every 200cans.If a quality control inspector finds a can without an expiration date,what is the probability that C fail to paste it?
since A pasted 30% of the cans,he failed to paste 70% of the cans.that is (70%)300.B pasted 15% and failed to paste 85% of the cans.that is (85%)250.C pasted 35% and failed to paste (65%)100.D pasted 7% and failed to paste (93%)150.E pasted 13% and failed to paste (87%)200.so if a quality control inspector finds a can without an expiration date,the probability that C failed to paste is (65%)100/(70%)300+(85%)250+(65%)100+(93%)150+(87%)200.
the answer is 0.5636
To find the probability that worker C fails to paste the expiration date given that a can is found without an expiration date, we need to use conditional probability.
Let's calculate the probability for each worker to fail to paste the expiration date:
Worker A: Fails once in every 300 cans, so the probability of failure is 1/300.
Worker B: Fails once in every 250 cans, so the probability of failure is 1/250.
Worker C: Fails once in every 100 cans, so the probability of failure is 1/100.
Worker D: Fails once in every 150 cans, so the probability of failure is 1/150.
Worker E: Fails once in every 200 cans, so the probability of failure is 1/200.
The total probability of a worker failing to paste the expiration date is the sum of these individual probabilities:
Total probability of failure = (1/300) + (1/250) + (1/100) + (1/150) + (1/200)
Let's calculate the total probability of failure:
Total probability of failure = (250 + 300 + 75 + 200 + 150) / (250 * 300 * 100 * 150 * 200)
= 975 / (22500000000)
= 1 / 23076923.08 (approximately)
Now, let's calculate the probability that worker C fails to paste the expiration date:
Probability of C failing = Probability of C failing AND any other worker failing
= (1/100) * (1 / 23076923.08)
= 1 / (100 * 23076923.08)
= 1 / 2307692300 (approximately)
Therefore, the probability that worker C fails to paste the expiration date, given that a can is found without an expiration date, is approximately 1 in 2,307,692,300.