If the probability of hitting a target on a single shot is 0.3, what is the probability that in 4 shots the target will be hit at least 3 times?
Solution
The probability of hitting a target on a single shot is $p = 0.3$. Number of shots targeted is $n=4$.
Let $X$ number of shots hot the target. $X\sim B(4, 0.3)$.
The probability mass function of $X$ is
$$ \begin{aligned} P(X=x) &= \binom{4}{x} (0.3)^x (1-0.3)^{4-x},\\ &\quad x=0,1,\cdots, 4. \end{aligned} $$
The probability that it will hit at least 3 times is
$$ \begin{aligned} P(X\geq 3) &= P(X=3) + P(X=4)\\ & =\binom{4}{3} (0.3)^{3} (1-0.3)^{4-3}+ \binom{4}{4} (0.3)^{4} (1-0.3)^{4-4}\\ &= 0.0756+ 0.0081\\ &= 0.0837 \end{aligned} $$
Further Reading
- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators
