Math  /  Discrete

QuestionTo choose the order of bands for the finals of a Battle of the Bands competition, Freddy puts a penny, a nickel, a dime, a quarter, and a half-dollar into five separate envelopes and has one band choose an envelope. The second band then chooses from the remaining envelopes. Draw a tree diagram to determine the sample space and find the probabilities for the selections of the two bands in the finals. Express probabilities as simplified fractions.
Part: 0/60 / 6 \square Part 1 of 6 (a) The sample space contains \square outcomes.

Studdy Solution

STEP 1

1. There are five different coins: a penny, a nickel, a dime, a quarter, and a half-dollar.
2. Each band selects one envelope containing a coin.
3. The order of selection matters, as each band chooses from the remaining envelopes.

STEP 2

1. Determine the total number of possible outcomes for the selection process.
2. Draw a tree diagram to visualize the sample space.
3. Calculate the probabilities for each selection outcome.

STEP 3

To find the total number of outcomes, consider the number of choices available for each band. The first band has 5 choices, and after one envelope is chosen, the second band has 4 remaining choices.

STEP 4

Calculate the total number of outcomes by multiplying the number of choices for the first band by the number of choices for the second band:
5×4=205 \times 4 = 20
Thus, the sample space contains 20 outcomes.
The sample space contains 20\boxed{20} outcomes.

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