Question

When randomly chosen, what will be the probability of the light not in green? Given that: A complete cycle of a traffic light takes $ 60 $ s. During each cycle the light is green for $ 25 $ s, yellow for $ 5 $ s and red for $ 30 $ s respectively.
(a) $ \dfrac{{12}}{7} $
(b) Cannot be determined
(c) $ \dfrac{7}{{12}} $
(d None of these

Answer 1

Hint: The given problem revolves around the concept of probability. So, we will use the definition of probability for each iteration/s for a given number of outcomes. The probability of an event A is denoted by ‘p (A)’ and the basic formula of finding probability is \[p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}}\] , where ‘n(s)’ denotes the favorable outcomes and ‘n(A)’ denotes the total number of outcomes for an respective event.

Complete step-by-step answer:
Since, the traffic light is fair, these outcomes have possibilities of getting all these three lights respectively; that is ‘RED’, ‘YELLOW’ and ‘GREEN’ probably.
Hence, we have given that
In a complete cycle of traffic light of $ 60 $ s, each light has probable of getting RED light for ‘ $ 30 $ ’ .seconds, YELLOW light for ’ $ 5 $ ’ seconds and GREEN light for ‘ $ 25 $ ’ seconds respectively
As a result, we know that
 \[{\text{Probability,}}p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}}\]
Where,
 $ n\left( A \right) = $ Total number of outcomes of an event that is, $ n\left( A \right) = 60 $ seconds
 $ n\left( s \right) = $ Individual outcome in an event, and
 $ p\left( A \right) = $ Probability of the required outcome
Hence, for probability of NOT GETTING ‘GREEN’ LIGHT that is $ \left( {{\text{RED + YELLOW}}} \right) $ in an event is,
 $ n\left( s \right) = 30 + 5 = 35 $ seconds
Substituting the values in the above formula, we get
 \[
  p\left( A \right) = \dfrac{{n\left( s \right)}}{{n\left( A \right)}} = \dfrac{{35}}{{60}} \\
  p\left( A \right) = \dfrac{7}{{12}} \\
 \]
 $ \Rightarrow $ Hence, the probability of not getting GREEN light $ \dfrac{7}{{12}} $ respectively.
 $ \therefore \Rightarrow $ Therefore, the correct option is (c)!
So, the correct answer is “Option c”.

Note: One should know the basic formula of probability while solving a question. We should also know the concepts of independent events and that their probabilities are not affected by each other’s occurrences. We should take care of the calculations so as to be sure of our final answer. Also, we should know that the sum of probabilities of all the possible events in a situation is one. That’s why, the sum of getting heads and tails on tossing a coin is one.