If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is:
0.25412184
Here we need to use the binomial theorem.
i.e. the probability of k successes out of total n experiments is calculated by the formula:
[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]
where p is the probability of successes.
Here we have p=Probability that signal is red.
i.e. p=15/50=3/10=0.3
Hence, 1-p=0.7
Also we have: n=8
and k=3
Hence,
[tex]P(X=3)=8_C_3\times (0.3)^3(0.7)^{8-3}\\\\\\P(X=3)=\dfrac{8!}{3!\times (8-3)!}\times (0.3)^3\times (0.7)^5\\\\\\P(X=3)=\dfrac{8!}{3!\times 5!}\times 0.00453789\\\\\\P(X=3)=0.25412184[/tex]
Hence, the probability is:
0.25412184
