Probabilidade de espaços amostrais para eventos compostos

Summary

In this engaging game show scenario, the contestant is faced with a vacation decision, choosing between three destinations: an Island, Skiing, and Camping, each with varying time options (1, 2, or 3 days). The goal is to calculate the probability of selecting a vacation that avoids snow, specifically choosing a destination that offers at least 2 days without snow. Through a step-by-step analysis, the presenter explains how to visualize the possibilities and compute the probability of the desired outcome, ultimately finding that there are 4 favorable outcomes out of 9 possible options, giving a probability of 4/9.

Takeaways

• 😀 The game show scenario involves choosing between three vacation destinations: an island, skiing, and camping.
• 😀 Each destination has three possible duration options: 1 day, 2 days, or 3 days.
• 😀 The objective is to calculate the total number of possible vacation combinations, which is 9 in total (3 destinations × 3 durations).
• 😀 The script illustrates how to organize and visualize the possibilities using a table.
• 😀 Each destination is linked to three possibilities: one for each duration (1 day, 2 days, 3 days).
• 😀 The total number of vacation outcomes is 9, with each outcome representing a unique combination of destination and duration.
• 😀 The game show involves drawing results randomly from a set of possibilities, assuming equal probability for each.
• 😀 The video presents a scenario where you prefer to avoid snow and want a vacation without skiing, which influences the selection process.
• 😀 The task is to calculate the probability of selecting a vacation where you spend at least 2 days away from snow, i.e., on an island or camping.
• 😀 Out of the 9 possibilities, 4 meet the condition of spending at least 2 days away from snow (island or camping).
• 😀 The final probability of the outcome is calculated as 4 out of 9, representing the chances of picking a non-skiing vacation with at least 2 days away from snow.

Q & A

What are the three vacation options in the game show scenario?

The three vacation options are an island, skiing, and camping.

How many days can you choose to spend at each vacation destination?

You can choose to spend 1, 2, or 3 days at each vacation destination.

What is the total number of possible vacation outcomes?

There are 9 possible outcomes, corresponding to the different combinations of destinations and days.

What is the goal of the contestant in terms of the vacation duration?

The contestant wants to have at least 2 days of vacation, specifically avoiding snow, which means not choosing skiing.

How do you calculate the probability of getting at least 2 days without snow?

To calculate the probability, count the number of favorable outcomes (at least 2 days without snow) and divide by the total number of possible outcomes. The probability is 4 favorable outcomes out of 9 total, so P = 4/9.

What destinations are considered favorable for the contestant's goal of avoiding snow?

The island and camping destinations are considered favorable, as skiing involves snow, which the contestant wants to avoid.

Why does the contestant want to avoid skiing?

The contestant lives in a cold place and does not want to experience snow, so they prefer a vacation without snow, like on an island or while camping.

What does the term 'space amostral' (sample space) refer to in the context of this game show?

'Space amostral' refers to the set of all possible outcomes that can occur in the game show. In this case, it includes all the combinations of destinations and durations (9 outcomes).

How can the possible outcomes be visualized?

The possible outcomes can be visualized in a table where rows represent the destinations (island, skiing, camping) and columns represent the number of days (1, 2, or 3).

How many outcomes correspond to the contestant's preference of at least 2 days without snow?

There are 4 favorable outcomes: 2 days and 3 days on the island, and 2 days and 3 days camping.