Question

A traffic light near a museum is green for 30 seconds, yellow for 5 seconds, and red for 15 seconds.

If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is

Answer 1

The answer I think maybe 8/3 this answer is a fraction of you are looking for one

Answer 2

If 8 vehicles approach the signal, the probability that 3 of them are stopped by the red light is:

0.25412184

Explanation:

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:

`P(X=k)=n_C_kp^k(1-p)^(n-k)`

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,

`P(X=3)=8_C_3* (0.3)^3(0.7)^(8-3)\\\\\\P(X=3)=(8!)/(3!* (8-3)!)* (0.3)^3* (0.7)^5\\\\\\P(X=3)=(8!)/(3!* 5!)* 0.00453789\\\\\\P(X=3)=0.25412184`

Hence, the probability is:

0.25412184