Question

Sam claims that his cat can do single-digit multiplication. He shows the cat 10 cards with simple multiplication problems that are either correct or incorrect. The cat correctly identifies the correctness of the card 7 times out of 10. If the cat were simply guessing, how many would the cat be expected to get correct?

Answer 1

Answer: The cat would expect 5 correct answers.

Explanation:

Since we have given that

Total number of cards = 10

Answers are either correct or incorrect.

and the cat correctly identifies the correctness of the card 7 times out of 10.

Expected value will be

`E(x)=\sum xp(x)`

Here, x is the number of answers and P(x) is the probability of getting correct answer.

Here, we have x = 10

Probability the cat would get correct =
`(1)/(2)`

So, expected value will be

`(1)/(2)* 10\\\\=5`

Hence, The cat would expect 5 correct answers.

Answer 2

The cat is expected to get correct is:

5

Explanation:

Sam claims that his cat can do single-digit multiplication.

He shows the cat 10 cards with simple multiplication problems that are either correct or incorrect.

Since, there are 50% chances of a question being correct or incorrect.

i.e. the probability of a answer being correct or incorrect is:

1/2

Also there are total 12 questions.

Hence, the expected value of the cat being correct after guessing is:

`E(x)=\sum xp(x)`

where x denote the event and the probability of an event.

Here x denote the question and p(x) it's probability.

Hence, the expected value is:

`(1)/(2)* 10=5`

Hence, the cat is expected to get correct is:

5