Math

QuestionA boy has a penny, nickel, dime, and quarter. What is the sample space for selecting 2 coins, and how many are there?

Studdy Solution

STEP 1

Assumptions1. The boy has four coins in his pocket a penny, a nickel, a dime, and a quarter. . He takes out two coins, one after the other.
3. The order in which the coins are taken out matters.

STEP 2

We need to list all possible outcomes of taking out two coins one after the other. This is known as the sample space.

STEP 3

Let's denote the penny as, the nickel as N, the dime as D, and the quarter as Q.

STEP 4

The possible outcomes when taking out the first coin are, N, D, Q.

STEP 5

For each of these outcomes, there are three remaining coins in the pocket. So, for each first coin, there are three possibilities for the second coin.

STEP 6

List all possible outcomes of taking out two coins one after the other.
The possible outcomes are (, N), (, D), (, Q), (,), (, D), (, Q), (,), (, N), (, Q), (Q,), (Q, N), (Q, D).

STEP 7

Count the total number of outcomes in the sample space.
There are12 possible outcomes.
The sample space is {(, N), (, D), (, Q), (,), (, D), (, Q), (,), (, N), (, Q), (Q,), (Q, N), (Q, D)} and the total number of outcomes is12.

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