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# New math GCSE question.

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1. "A company makes tiles after manufacture pairs of tiles are tested. The probability that at least one of these tiles is cracked is 0.9996. How many tiles would the company expect to be cracked in a batch of 1000?" Does anybody have any ideas on how to work this out, it's question 24 on an AQA collins mock paper so it's one of the hardest considering this paper has 25 questions. Any help would be appreciated, thanks!
2. 0.9996 x 1000 = 999.6 tiles broken
3. (Original post by Nuggetsarelife)
0.9996 x 1000 = 999.6 tiles broken
Thank-you! Does this still apply since the tests were on a pair of tiles and the 0.996 was the probability that at least one of the tiles was cracked?
4. (Original post by jasmine_GCSE)
Thank-you! Does this still apply since the tests were on a pair of tiles and the 0.996 was the probability that at least one of the tiles was cracked?
I'm not sure that answer is correct. The company tests them in pairs and the chance of one of the two tiles being broken is 0.9996.

So we're working with 500 tests (since 1000 tiles divided into pairs). The chance of one of the tiles being broken in each test is 0.9996, so that would leave us with 500*0.9996 to get your answer.
5. (Original post by Macalese)
I'm not sure that answer is correct. The company tests them in pairs and the chance of one of the two tiles being broken is 0.9996.

So we're working with 500 tests (since 1000 tiles divided into pairs). The chance of one of the tiles being broken in each test is 0.9996, so that would leave us with 500*0.9996 to get your answer.
This is what I initially thought as well but the wording of the question made me unsure since the words at least were in bold in accordance to "The probability that at least one of these pairs is cracked is 0.9996"
6. (Original post by jasmine_GCSE)
This is what I initially thought as well but the wording of the question made me unsure since the words at least were in bold in accordance to "The probability that at least one of these pairs is cracked is 0.9996"
Does the question say "The probability that at least one of these pairs is cracked is 0.9996" or does it say "The probability that at least one of these tiles is cracked is 0.9996."? Your info in your original post is different to what you've said there!
7. (Original post by Macalese)
Does the question say "The probability that at least one of these pairs is cracked is 0.9996" or does it say "The probability that at least one of these tiles is cracked is 0.9996."? Your info in your original post is different to what you've said there!
Sorry for the confusion! The exact wording of the questions is "A company makes tiles. After manufacture pairs of tiles are tested. The probability that at least one of these pairs is cracked is 0.9996. How many tiles would the company expect to be cracked in a batch of 1000?"
8. (Original post by jasmine_GCSE)
Sorry for the confusion! The exact wording of the questions is "A company makes tiles. After manufacture pairs of tiles are tested. The probability that at least one of these pairs is cracked is 0.9996. How many tiles would the company expect to be cracked in a batch of 1000?"
That is such an awfully worded question.

I assume "The probability that at least one of these pairs is cracked is 0.9996" means one tile in each pair? If so you've got 500 pairs in the batch of 1000, the chance one of these is cracked is 0.9996 so 500*0.9996=499.8. So you're expecting at least 500 cracked tiles?

It might take someone with better English than me to solve that riddle.
9. (Original post by Macalese)
That is such an awfully worded question.

I assume "The probability that at least one of these pairs is cracked is 0.9996" means one tile in each pair? If so you've got 500 pairs in the batch of 1000, the chance one of these is cracked is 0.9996 so 500*0.9996=499.8. So you're expecting at least 500 cracked tiles?

It might take someone with better English than me to solve that riddle.
I know! The wording on all of the new GCSE math questions is very confusing! Thankyou for your help, I have worked it out as 499.8 as well so I will just stick with that. I expect the teacher will go over it in class so I can check then. Thanks a lot!
10. (Original post by jasmine_GCSE)
I know! The wording on all of the new GCSE math questions is very confusing! Thankyou for your help, I have worked it out as 499.8 as well so I will just stick with that. I expect the teacher will go over it in class so I can check then. Thanks a lot!
The probability that either of them in the pair is cracked = 0.9996 (1)
=> the probability that none of them in the pair is cracked = 1 - 0.9996 = 0.0004 (2)
=> the probability that any one tile is not cracked = sqrt(0.0004) = 0.02 (3)

Equation 1 is given in the question. Equation 2 is found because of how NOT A AND NOT B is the inverse of A OR B. Equation 3 is found based on the rule that the P (A AND B) = P(A) * P(B). So therefore P(Both not cracked) = P(any one not cracked) * P (any one not cracked). P(any one not cracked) = sqrt(P(Both not cracked)

=> Expected number of tiles not cracked = 0.02 * 1000 = 20
=> Expected tiles cracked = 1000 - 20 = 980.
11. (Original post by BobBobson)
The probability that either of them in the pair is cracked = 0.9996 (1)
=> the probability that none of them in the pair is cracked = 1 - 0.9996 = 0.0004 (2)
=> the probability that any one tile is not cracked = sqrt(0.0004) = 0.02 (3)

Equation 1 is given in the question. Equation 2 is found because of how NOT A AND NOT B is the inverse of A OR B. Equation 3 is found based on the rule that the P (A AND B) = P(A) * P(B). So therefore P(Both not cracked) = P(any one not cracked) * P (any one not cracked). P(any one not cracked) = sqrt(P(Both not cracked)

=> Expected number of tiles not cracked = 0.02 * 1000 = 20
=> Expected tiles cracked = 1000 - 20 = 980.
Wow thanks this is very helpful!!!

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