Answer:
The expected number of cards is 6.
Step-by-step 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,
\(P(C)=\frac{1}{2}\)
And, the probability of incorrect card,
\(P(C')=\frac{1}{2}\)
Thus, the expected number of cards = expected number of correct card + expected number of incorrect card
= n(C) × P(C) + n(C') × P(C')
\(=9\times \frac{1}{2}+3\times \frac{1}{2}\)
\(=\frac{9}{2}+\frac{3}{2}\)
\(=\frac{12}{2}=6\)
