The probability of 2 success among 5 trials is 0.132.
Solution:
Given n = 5, x = 2, p = 0.70
Binomial distribution formula:
The probability of x success in n trials is
[tex]P(X)={C^n_x}\ p^x\ q^{n-x}[/tex]
where p is the probability of success and q is the probability of failure,
q = 1 –p
= 1 – 0.70
q = 0.30
Therefore, the probability of 2 success among 5 trials is
[tex]P(X)={C^5_2}\ (0.70)^2\ (0.30)^{5-2}[/tex]
[tex]$=\frac{5\times 4}{1 \times 2} \times \ (0.70)^2\ \times(0.30)^3[/tex]
[tex]$=10 \times \ 0.49\times 0.027[/tex]
[tex]P(X)=0.1323[/tex]
P(X) ≈ 0.132 (Round to three decimal)
Hence the probability of 2 success among 5 trials is 0.132.
