Question

Suppose that the event of picking a face card from a standard deck of 52 cards is considered a success. If a card is drawn at random and replaced, and this process is repeated 11 times, what is the probability that the card selected was a face card 6 times?
a. 0.019
b. 0.024
c. 0.004
d. 0.976
e. 0.995

Answer 1

Answer:

0.019

Step-by-step explanation:

Number of face cars = 12

Total number of cards =52

So, Probability of getting face card = $\frac{12}{52}$

Probability of not getting face card = $1-\frac{12}{52}=\frac{40}{52}$

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 : $P(X=r)=^nC_r p^r q^{n-r}$

p  = probability of success = $\frac{12}{52}$

q = Probability of failure =$\frac{40}{52}$

n = no. of trials = 11

r = no. of times getting success = 6

Substitute then values in the formula

$P(X=6)=^{11}C_6 (\frac{12}{52})^6 (\frac{40}{52})^{11-6}$

$P(X=6)=^{11}C_6 (\frac{12}{52})^6 (\frac{40}{52})^{5}$

$P(X=6)=0.019$

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.

Answer 2

I think it might be d or e    0.995 or 0.976