Question

You have won the lottery The van with the balloons, and oversized check roiled up to your home and you've been handed a million dollars cash. But there's a catch-each year, you have to go to Vegas and play a game of high-stakes blackpack. There's a 50% chance that you'l double your meney each year, and theres a 50% chance that your lose had of it This goes on once a year for two years, and only after that can you begin to spend the money, At the end of two years (after two farnes), what's the probability that you have exactly 4 million dollars? Use a tree diagram to figure out the answres

Write your answer as a percentage.

Answer 1

25%

Explanation:

A tree diagram would look something like this:

Win Win

Win Loss Win Loss

with each branch having probability 1/2.

Since we want the case for 4 million dollars (1 million doubled two times with two wins), the probability is 1/2 * 1/2 = 1/4 = 25%.

Answer 2

Step-by-step explanation: To calculate the probability of having exactly 4 million dollars at the end of two years of playing high-stakes blackjack, we can use a tree diagram.

In the first year, there are two possible outcomes: you can either double your money or lose half of it. Let's represent these outcomes as "D" for double and "L" for lose. After the first year, you will either have 2 million dollars or 500,000 dollars.

In the second year, the same possibilities exist for both outcomes from the first year. So, we have four branches for each possible outcome: DD, DL, LD, and LL.

Let's calculate the probabilities for each branch:

- DD: This means you doubled your money twice, resulting in 2 million dollars becoming 4 million dollars. The probability of this happening is 0.5 * 0.5 = 0.25.

- DL: This means you doubled your money in the first year and then lost half of it in the second year. The probability of this happening is 0.5 * 0.5 = 0.25.

- LD: This means you lost half of your money in the first year and then doubled it in the second year. The probability of this happening is 0.5 * 0.5 = 0.25.

- LL: This means you lost half of your money twice, resulting in 500,000 dollars becoming 250,000 dollars. The probability of this happening is 0.5 * 0.5 = 0.25.

To calculate the probability of having exactly 4 million dollars at the end of two years, we add up the probabilities of the DD branch: 0.25. Therefore, the probability is 25%.

Keep in mind that this calculation assumes the probabilities of winning or losing each year are independent of the previous year's outcomes. It's important to note that gambling involves chance, and the actual outcomes may differ from the calculated probabilities.