Questions: A box contains three cards. On one card there is an apple (A), on another card there is a sun ( S ), and on the third card there is a moon (M). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below. a) Determine the number of sample points in the sample space. There are points in the sample space.

A box contains three cards. On one card there is an apple (A), on another card there is a sun ( S ), and on the third card there is a moon (M). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below.
a) Determine the number of sample points in the sample space.

There are points in the sample space.

Transcript text: A box contains three cards. On one card there is an apple (A), on another card there is a sun ( S ), and on the third card there is a moon (M). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below. a) Determine the number of sample points in the sample space. There are $\square$ points in the sample space.

Solution

Solution Steps

To determine the number of sample points in the sample space when two cards are selected at random with replacement, we need to consider that each selection is independent and each card can be selected again. Since there are 3 cards and each card can be selected twice, the total number of sample points is the product of the number of choices for each selection.

Step 1: Determine the Number of Sample Points

When selecting two cards from a set of three cards (A, S, M) with replacement, each selection is independent. The total number of sample points in the sample space can be calculated using the formula:

\[ \text{Number of sample points} = \text{Number of cards}^{\text{Number of selections}} = 3^2 \]

Step 2: Calculate the Total

Calculating $3^2$:

\[ 3^2 = 9 \]