Answer:
0.019
Step-by-step explanation:
Number of face cars = 12
Total number of cards =52
So, Probability of getting face card = [tex]\frac{12}{52}[/tex]
Probability of not getting face card = [tex]1-\frac{12}{52}=\frac{40}{52}[/tex]
Now we are given that a card is drawn at random and replaced, and this process is repeated 11 times so, what is the probability that the card selected was a face card 6 times
So, we will use binomial
Success is getting a face card
Failure is not getting a face card
Formula : [tex]P(X=r)=^nC_r p^r q^{n-r}[/tex]
p = probability of success = [tex]\frac{12}{52}[/tex]
q = Probability of failure =[tex]\frac{40}{52}[/tex]
n = no. of trials = 11
r = no. of times getting success = 6
Substitute then values in the formula
[tex]P(X=6)=^{11}C_6 (\frac{12}{52})^6 (\frac{40}{52})^{11-6}[/tex]
[tex]P(X=6)=^{11}C_6 (\frac{12}{52})^6 (\frac{40}{52})^{5}[/tex]
[tex]P(X=6)=0.019[/tex]
Hence If a card is drawn at random and replaced, and this process is repeated 11 times, the probability that the card selected was a face card 6 times is 0.019.
