A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that exactly 8 tails occur is 0.1963.
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The probability of a tail occurring is 0.5, while the probability of a tail, not coming is 0.5, therefore, we can write p=0.5 and q=0.5.
Now, the probability of exactly 8 tails occurring can be written as,
P(X=8) = ¹⁶C₈ (0.5)⁽⁸⁾ (0.5)⁽¹⁶⁻⁸⁾
P(X=8) = 12,870 (0.5)¹⁶
P(X=8) = 0.1963
Hence, the probability that exactly 8 tails occur is 0.1963.
Learn more about Binomial Distribution:
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