- #1

Master1022

- 611

- 117

- Homework Statement
- (a) What is the probability of picking up ONLY one jack when taking 5 cards from a 52 card deck

(b) Considering that in the first 3 cards there is a jack what is the probability that the jack was the first card to be extracted

- Relevant Equations
- Probability and combinatorics

Hi,

I was looking through probability questions and attempting it.

(a) What is the probability of picking up ONLY one jack when taking 5 cards from a 52 card deck

(b) Considering that in the first 3 cards there is a jack what is the probability that the jack was the first card to be extracted

For part (a), I did:

[tex] \text{probability} = \frac{\text{number of ways of picking up 5 cards with only 1 jack}}{\text{total number of ways of picking up 5 cards from 52 cards}} [/tex]

[tex] P = \frac{\begin{pmatrix} 4 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 52 - 4 \\ 4 \end{pmatrix}}{\begin{pmatrix} 52 \\ 5 \end{pmatrix}} = \frac{\begin{pmatrix} 4 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 48 \\ 4 \end{pmatrix}}{\begin{pmatrix} 52 \\ 5 \end{pmatrix}} [/tex]

The terms in the numerator represent:

- ##\begin{pmatrix} 4 \\ 1 \end{pmatrix}## is the number of jack's available

- ##\begin{pmatrix} 48 \\ 4 \end{pmatrix}## is the number of ways to pick the remaining 4 cards from 48 non-jack cards in the deck.

Does this look right for (a)?

For part (b), I thought it would be ##\frac{1}{3}##, but I may need to give this more thought...

Thanks in advance.

I was looking through probability questions and attempting it.

**Question:**(a) What is the probability of picking up ONLY one jack when taking 5 cards from a 52 card deck

(b) Considering that in the first 3 cards there is a jack what is the probability that the jack was the first card to be extracted

**Attempt:**For part (a), I did:

[tex] \text{probability} = \frac{\text{number of ways of picking up 5 cards with only 1 jack}}{\text{total number of ways of picking up 5 cards from 52 cards}} [/tex]

[tex] P = \frac{\begin{pmatrix} 4 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 52 - 4 \\ 4 \end{pmatrix}}{\begin{pmatrix} 52 \\ 5 \end{pmatrix}} = \frac{\begin{pmatrix} 4 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 48 \\ 4 \end{pmatrix}}{\begin{pmatrix} 52 \\ 5 \end{pmatrix}} [/tex]

The terms in the numerator represent:

- ##\begin{pmatrix} 4 \\ 1 \end{pmatrix}## is the number of jack's available

- ##\begin{pmatrix} 48 \\ 4 \end{pmatrix}## is the number of ways to pick the remaining 4 cards from 48 non-jack cards in the deck.

Does this look right for (a)?

For part (b), I thought it would be ##\frac{1}{3}##, but I may need to give this more thought...

Thanks in advance.