Question

Andy claims that his bird can do single-digit multiplication. He shows the bird 12 cards with simple multiplication problems that are either correct or incorrect. The bird correctly identifies the correctness of the card 9 times out of 12. If the bird were simply guessing, how many would the bird be expected to get correct? 3 9 6

Answer 1

I believe the answer is 6

Answer 2

The expected number of cards is 6.

Explanation:

We know that,

'Expected value = Total number of trials × Probability of each trial'

Let C is the event of correct cards and C' is the event of incorrect cards.

Given,

Total number of cards = 12

Also, the correctness of the card is 9 times out of 12,

Thus, the number of correct cards,

n(C) = 9,

⇒ The number of incorrect cards,

n(C') = 12 - 9 = 3

Also, A card can be can be correct or incorrect,

Thus, The probability of correct card,

`P(C)=(1)/(2)`

And, the probability of incorrect card,

`P(C')=(1)/(2)`

Thus, the expected number of cards = expected number of correct card + expected number of incorrect card

= n(C) × P(C) + n(C') × P(C')

`=9* (1)/(2)+3* (1)/(2)`

`=(9)/(2)+(3)/(2)`

`=(12)/(2)=6`