Brian claims that his dog can do single-digit multiplication. he shows the dog 10 cards with simple multiplication problems that are either correct or incorrect. the dog correctly identifies the correctness of the card 7 times out of 10. if the dog were simply guessing, how many would the dog be expected to get correct?
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This is a question on probability.
There are 10 cards .
The probability of the dog identifying the correctness is 7 / 10
The probability of not identifying the correctness is 3/10
When the correctness of the card is identified :
From a tree diagram, the probability of getting it correct or wrong is 1/2 since the total possible outcomes is 2.
The probability of getting the expected answers correct is thus:
1 / 2 of 7 / 10 = 7 / 20
The total number of cards is 10 and so the total cards which were correctly identified are:
7 / 20 × 10 = 3.5
Since we do not have a half a card we round this off to a whole number :
We get 4 cards. as the answer.
There are 10 cards .
The probability of the dog identifying the correctness is 7 / 10
The probability of not identifying the correctness is 3/10
When the correctness of the card is identified :
From a tree diagram, the probability of getting it correct or wrong is 1/2 since the total possible outcomes is 2.
The probability of getting the expected answers correct is thus:
1 / 2 of 7 / 10 = 7 / 20
The total number of cards is 10 and so the total cards which were correctly identified are:
7 / 20 × 10 = 3.5
Since we do not have a half a card we round this off to a whole number :
We get 4 cards. as the answer.
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