Answer:
53.7 %
Step-by-step explanation:
Given:
Number of trials, [tex]n=7[/tex]
Number of successes, [tex]x=2,3[/tex]
Probability of success, [tex]p=42 \%= \frac{42}{100}=0.42[/tex]
Therefore, probability of failure, [tex]q=1-p=1-0.42=0.58[/tex]
The Bernoulli's distribution for [tex]x[/tex] successes out of [tex]n[/tex] trials is given as:
[tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{(n-x)}[/tex]
So, probability of 2 or 3 successes is given as:
[tex]P(X=2\textrm{ or}X=3)=P(X=2)+P(X=3)\\\\P(X=2\textrm{ or}X=3)=_{2}^{7}\textrm{C}(0.42)^{2}(0.58)^{(7-2)}+_{3}^{7}\textrm{C}(0.42)^{3}(0.58)^{(7-3)}\\\\P(X=2\textrm{ or}X=3)=21\times (0.42)^{2}(0.58)^{5}+35\times (0.42)^{3}(0.58)^{4}\\\\P(X=2\textrm{ or}X=3)= 0.5365=53.65 \% \approx 53.7 \%[/tex]
Therefore, the probability of 2 or 3 successes in 7 trials of a binomial experiment is 53.7 %.
