Questions & Answers

Question

Answers

A). What is the probability of getting the letter A?

B). What is the probability of not getting an A?

Answer

Verified

128.4k+ views

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} $