Question

Kyle stands on a street corner tossing a coin . He decides he will toss the coin 10 times , each time walking 1 block north if it lands heads up, and 1 block south if it lands tails up . Find the probability that he ends up 2 blocks south of his original corner ( the probability is , round to the nearest thousandth as needed. )

Answer 1

Explanation:

Kyle tosses the coin 10 times.

2. Assign a direction for each outcome: Heads represents moving 1 block north, and tails represents moving 1 block south.

3. Consider the outcome of each coin toss and determine the direction Kyle moves:

- Coin toss 1: Let's say it lands heads up. Kyle moves 1 block north.

- Coin toss 2: Let's say it lands tails up. Kyle moves 1 block south.

- Coin toss 3: ...

- Continue this process for all 10 coin tosses, determining the direction Kyle moves based on the outcome.

4. Calculate the final position by adding up the total number of blocks moved in each direction:

- If Kyle moved north (heads) 6 times and south (tails) 4 times, he moved a total of 6 blocks north and 4 blocks south.

- Therefore, his final position is 6 blocks north - 4 blocks south = 2 blocks north.

Therefore, after tossing the coin 10 times, Kyle will be 2 blocks north from his starting position on the street corner.