Question

Blessy has two bags containing numbered counters.

She takes one counter at random from bag A and another counter at random from Bag B. She adds the numbers on her two counters. Find the probability that Blessy’s answer is more than 6.

Answer 1

Hint : In this question, we need to determine the probability that Blessy’s answer was more than 6 when she had drawn 2 balls at random from the bags A and B. For this, we will use the basic formula of probability which is given as $P(E) = \dfrac{{n(F)}}{{n(A)}}$.

Complete step by step solution:
A total number of events of drawing counters from bag A and bag B having 5 counters and 4 counters respectively is the product of the total counters in the bags.
Let the total number of events be $n(A)$.
So, the total number of events is given as: $n(A) = 5 \times 4 = 20 - - - - (i)$
Now, a favourable number of events are the events satisfying the given condition in the question. Here, the condition is that the total sum of the counters should be more than 6.
So, the favourable number of outcomes is given as:
n(F) = \left\\{ {\left( {1,6} \right);\left( {2,6} \right);\left( {3,4} \right);\left( {3,6} \right);\left( {4,3} \right);\left( {1,6} \right);\left( {4,4} \right);\left( {4,6} \right)} \right\\} = 8 - - - - (ii)

Now, the ratio of the favourable number of outcomes to the total number of outcomes results in the probability of satisfying the favourable outcomes. Mathematically $P(E) = \dfrac{{n(F)}}{{n(A)}}$. Here, a favourable number of outcomes is 8, and the total number of outcomes is 20.
So, substitute $n(F) = 8{\text{ and }}n(A) = 20$ in the formula $P(E) = \dfrac{{n(F)}}{{n(A)}}$ to determine the probability that Blessy’s have more than 6 as the sum of the counters.

$$P(E) = \dfrac{{n(F)}}{{n(A)}} \\\ = \dfrac{8}{{20}} \\\ = \dfrac{2}{5} \\\ = 0.4 \\\$$

Hence, the probability that Bleesy has the sum of the counters in her hand is 0.4.

Note : Students must be careful while estimating the total number of favourable outcomes as if even one favourable outcome has not been counted then, it will lead to the wrong answer.