There are two possible ways for X=1: first light is green and second is red OR first light is red and second is green. The probabilities for these two options are to be summed: 0.6*0.4 + 0.4*0.6 to give the probability of exactly one light being green, namely 0.48.
P(X = 1) = 0.48
"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
"It is a probability distribution that gives only two possible results in an experiment, either success or failure. "
[tex]P(x)=n_C_x\times (p)^{x}\times (q)^{n-x}[/tex], here n is the total number of outcomes, 'p' is the probability of success and 'q' is the probability of failure
For given example,
The probability that traffic lights on a certain road will be green is 0.6
This means, the probability of success (p) = 0.6
So, the probability of failure (q) = 1 - p
q = 0.4
When a driver on that road approaches two traffic lights in a row, X is the number of traffic lights that are green.
here, n = 2, p = 0.6, q = 0.4, x = 1
Using the formula of Binomial distribution the required probability is,
[tex]P(x=1)=2_C_1\times (0.6)^{1}\times (0.4)^{2-1}\\\\P(x=1)=\frac{2!}{1!\times (2-1)!}\times 0.6\times 0.4^1\\\\P(x=1)=2\times 0.6\times 0.4\\\\\bold{P(x=1)=0.48}[/tex]
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