Chapter 7.1, Problem 7.17E

(a)

To determine

To Explain: the assumptions for the chance behaviour involved in this setting.

Answer to Problem 7.17E

Independent draws, constant probability of success

Explanation of Solution

Given:

Drawing cards until draw an ace (after drawing a card from deck placed back)

Cards are shuffled after every card is replaced which should make sure that cards are arbitrary drawn. It needs that all draws of the cards would be independent, which is satisfied when the cards are thoroughly shuffled.

It also requires that each card has the same chance of selecting

(b)

To determine

To Explain: that assign digits to represent outcomes.

Answer to Problem 7.17E

Ace: Numbers 00 to 03

Not Ace: Number 04 to 51

Ignore: Number 52 to 100

Explanation of Solution

Given:

Total sample space =52 cards

Favourable cases = 4 cards are aces

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

(c)

To determine

To Calculate: the estimate probability and simulate 10 repetitions using your calculator or Table B.

Answer to Problem 7.17E

0.7

Explanation of Solution

Formula used:

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

Calculation:

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)