C. A game show contestant has four doors
from which to choose. Behind one door
is a valuable prize. Behind the other
doors is worthless junk. What is the
probability that the valuable prize will be
chosen? Give your answer as a ratio and
a percent.

Question

UpStudy AI · Accepted Answer

To find the probability that the contestant will choose the door with the valuable prize, we can follow these steps:

1. **Identify the total number of doors**: There are 4 doors in total.
2. **Identify the number of doors with a prize**: There is 1 door with a valuable prize.

### Step 1: Calculate the Probability as a Ratio
The probability $$ P $$ of choosing the door with the prize can be calculated using the formula:

$$
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{4}
$$

### Step 2: Convert the Ratio to a Percent
To convert the ratio to a percent, we multiply by 100:

$$
P_{\text{percent}} = \frac{1}{4} \times 100
$$

Now, let's calculate the percent.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{4}\times 100$$
- step1: Reduce the numbers:
  $$1\times 25$$
- step2: Simplify:
  $$25$$
The probability of choosing the door with the valuable prize is:

- As a ratio: $$ \frac{1}{4} $$
- As a percent: $$ 25\% $$

Thus, the contestant has a $$ \frac{1}{4} $$ chance or a $$ 25\% $$ chance of selecting the door with the valuable prize.
The probability of choosing the valuable prize is $$ \frac{1}{4} $$ or 25%.

C. A game show contestant has four doors
from which to choose. Behind one door
is a valuable prize. Behind the other
doors is worthless junk. What is the
probability that the valuable prize will be
chosen? Give your answer as a ratio and
a percent.

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C. A game show contestant has four doors from which to choose. Behind one door is a valuable prize. Behind the other doors is worthless junk. What is the probability that the valuable prize will be chosen? Give your answer as a ratio and a percent.

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Solución

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preguntas relacionadas

Latest Probability Questions

C. A game show contestant has four doors
from which to choose. Behind one door
is a valuable prize. Behind the other
doors is worthless junk. What is the
probability that the valuable prize will be
chosen? Give your answer as a ratio and
a percent.