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The letters of the word MALAYALAM are written in paper slip and put into a box. A child is asked to take one slip from the box without looking.
A). What is the probability of getting the letter A?
B). What is the probability of not getting an A?

Last updated date: 13th Jun 2024
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Hint: Here just by reading the Question we got to know it’s the question of probability. We know the probability is nothing but a ration. We’ll use a probability formula to solve the first part of the question. Then we’ll use Sum of, probability of occurring an event, and the probability of not occurring that event is equal to 1.

Complete step-by-step solution:
Probability tells us how likely an event will occur. It is a ratio of the number of favorable cases to the number of total cases. That is
$P(E) = \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Number of total cases}}}}$
Here, E is an event for which we are calculating the probability.
According to the question, getting a letter A is the event. For this event, we’ll first calculate the number of favorable cases and the number of total cases.
Observe that in the MALAYALAM word, 4 times A is occurring. It means there are 4 cases in our favor. Whereas, there are 9 total letters in the MALAYALAM word. It means the total number of cases is 9.
Now, putting these values into the formula of probability we get,
 $P(E) = \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Number of total cases}}}} = \dfrac{4}{9}$
Hence, the Probability of getting A letter is $\dfrac{4}{9}$.
(b) For the second part we’ll use the formula $P(E) + P({E^{'}}) = 1$, where $P({E^{'}})$represents probability of not occurring an event. As we mentioned earlier our event is getting the letter A. So, ${E^{'}}$ will be “not getting A”. We already have the value of $P(E)$ from the first part. On putting the value in the formula, we get,
$ P(E) + P({E^{‘}}) = 1 $
$ \Rightarrow \dfrac{4}{9} + P({E^{'}}) = 1\;\;\;\;\;\; [P(E) = \dfrac{4}{9}] $
$ \Rightarrow P({E^{'}}) = 1 - \dfrac{4}{9} $
$\Rightarrow P({E^{'}}) = \dfrac{{9 - 4}}{9} $
  $ \Rightarrow P({E^{'}}) = \dfrac{5}{9} $

Hence, the probability of not getting an A is $\dfrac{5}{9}$.

Note: Probability is the core phenomenon of predictive analysis. It has several variations. For example, the Situation in this question will be safe and they can ask for different probabilities. Like the probability of getting A on the second pick. Probability of getting M, the probability of getting a vowel or consonant. These are some variations of the given questions.