Answered

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?

A0.019
B0.024
C0.004
D0.976
E0.995

Verified Answer :

emanueltezera

i think it might be d or e    0.995 or 0.976

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.

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