Question

In the playing card deck below what is the chance of pulling 5 face cards without replacing the cards in between pulls? Answer in decimal form rounded to the 6th digit after the decimal

Answer 1

Given the question in the question tab, the following are the steps to solve the questions.

Step 1: State the formula for probability

`\text{Probability}=\frac{no\text{ of outcomes}}{sample\text{ space}}`

Step 2: Write out the known parameters

In a playing card deck, there are 52 playing cards. This becomes the Sample space. In a playing card deck, there are 12 face cards. Pulling without replacement means that the cards reduce by 1 after each successive pull of cards, i.e, (n-1).

Step 3: Calculate the chance of pulling 5 cards without replacing the cards in between pulls.

`\begin{gathered} \text{Probability}=\frac{no\text{ of outcomes}}{sample\text{ space}} \\ P(5face\text{ cards without replacement)=P(face card 1) and P(face card 2) and} \\ \text{P(face card 3) and P(face card 4) and P(face card 5)} \\ P(5face\text{ cards without replacement)}=(12)/(52)*(11)/(51)*(10)/(50)*(9)/(49)*(8)/(48) \\ P(5face\text{ cards without replacement)}=(33)/(108290) \\ P(5face\text{ cards without replacement)}=0.000304737 \\ P(5face\text{ cards without replacement)}\approx0.000305 \end{gathered}`

Hence, the chance of pulling 5 face cards without replacing the cards in between pulls approximately to 6 decimal places is 0.000305.