Final answer:
To find the probability of obtaining a certain number of heads when flipping a fair coin 20 times, use the binomial probability formula. With the formula P(X=k) = 20Ck × (0.5)^k × (0.5)^(20-k), you can calculate for any number of heads, where 'k' is the desired number of heads.
Step-by-step explanation:
The probability of getting a specific number of heads when flipping a fair coin multiple times can be calculated using the binomial probability formula:
P(X=k) = nCk × p^k × (1-p)^(n-k)
where:
- n = total number of flips
- k = number of successful outcomes (heads in this case)
- p = probability of getting heads on a single flip
- nCk = number of combinations of n things taken k at a time
For a fair coin, the probability of heads (p) is 0.5. Hence:
- For exactly 9 heads (k=9), the calculation is:
P(9 heads) = 20C9 × (0.5)^9 × (0.5)^(20-9)
- For exactly 10 heads (k=10), the calculation is:
P(10 heads) = 20C10 × (0.5)^10 × (0.5)^(20-10)
- For exactly 11 heads (k=11), the calculation is:
P(11 heads) = 20C11 × (0.5)^11 × (0.5)^(20-11)
To find the exact values, you would calculate the binomial coefficients and multiply by the appropriate powers of 0.5.