Chapter 7.1, Problem 7.26E

(a)

To determine

To Calculate: the probability of drawing an ace in 10 draws be higher, lower and explain.

Explanation of Solution

Given:

Drawing cards until drawing an ace (not placing back to the deck after a draw)

Cards are not placing back to the deck after drawing the card drawn. This means that the probability of drawing an ace increases after non-ace cards were drawn as there are very less non-ace cards in the deck.

Combined probability of drawing an ace in the first 10 draws will then be higher, because it would be more likely to draw an ace on the second, third, forth....and so on.

(b)

To determine

To find: the design and carry out 10 repetitions of a simulation to imitate the chance behaviour in this new setting and describe the steps in simulation.

Answer to Problem 7.26E

0.7

Explanation of Solution

Given:

Total sample space =52 cards

Favourable cases = 4 cards are aces

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

Total 4 numbers of Aces and 48 other number to non-ace cards

Ace: Numbers 00 to 03

Not Ace: Number 04 to 51

Ignore: Number 52 to 99

Using the calculator generating one set of 10 draws using TI 83/TI 84 calculator

  $randInt\left(0,52,10\right)$

Drawing the cards until getting an ace and observed if draws an ace or not. Repeating this 9 more times

No ace, Ace, Ace, Ace, Ace, Ace, Ace, Ace, No Ace, No Ace

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ P\left(Ace\right)=\frac{7}{10}\\ =0.7\end{array}$

Therefore the estimate probability is 0.7 (may vary)