6. Suppose you are playing a game of darts. The probability of success is 0.8. Calculate what will be the probability that you will hit the dartboard on the fifth try? give the formula to get 0.8

1. We are using the geometric distribution to model this scenario, where the probability of success on each try is 0.8.
2. The formula for the probability of the first success on the nth trial is given by:
P(X = n) = (1-p)^{n-1} \cdot p
where \( p = 0.8 \) is the probability of success.
3. Substitute the given values into the formula:
P(X = 5) = (1 - 0.8)^{5-1} \cdot 0.8
4. Simplify the expression:
P(X = 5) = (0.2)^4 \cdot 0.8
5. Calculate the result:
P(X = 5) = 0.00128

- Hence, the probability that you will hit the dartboard on the fifth try is \( 0.00128 \).