Question

if you get 20 points for a coin flip landing on heads and 10 points for it landing on tails, what is the probability that after 8 throws of the coin, the sum of your points is 100?

Answer 1

To find the probability of getting a sum of 100 points after 8 coin tosses, we can use the combination formula to count the number of favorable outcomes. The probability is found to be 0.21875, or 21.875%.

Step-by-step explanation:

To find the probability of getting a sum of 100 points after 8 coin tosses, we need to consider all the possible outcomes.

Let's denote 'H' as heads (20 points) and 'T' as tails (10 points).

The sum of points after 8 tosses can range from 80 points (all tails) to 160 points (all heads). We need to find the number of favorable outcomes when the sum is 100 points.

We can solve this by finding the number of combinations of heads and tails that add up to 100 using stars and bars.

Using the formula for combinations, we can calculate:

C(k, n) = (n + k - 1) C (k-1)

Where n is the total number of tosses and k is the number of heads.

Using this formula, we find that the number of combinations is C(8, 5) = 56.

Therefore, the probability of getting a sum of 100 points after 8 tosses is 56/(2^8) = 0.21875, or 21.875%.