The probability of obtaining $4$ heads, $4$ tails when $8$ unbiased coins are tossed is :
- $\dfrac{1}{2}$
- $\dfrac{C_{4}^{8}}{2^{8}}$
- $\dfrac{C_{0}^{8}}{2^{8}}$
- $\dfrac{1}{4}$
The probability of getting exactly k successes in n Bernoulli trials is given by the binomial distribution formula: C(n, k) * p^k * (1-p)^(n-k). For 8 unbiased coins, n=8, k=4, and p=1/2, so the probability is C(8, 4) * (1/2)^4 * (1/2)^4, which simplifies to C(8, 4) / 2^8.
Using the binomial probability formula, the probability of obtaining exactly 4 heads and 4 tails in 8 tosses is found by the combination of 8 items taken 4 at a time divided by 2 to the power of 8. The combination of 8 items taken 4 at a time is 70, and 2 to the power of 8 is 256. Therefore, the probability is the combination of 8 items taken 4 at a time divided by 2 to the power of 8.