Question

A basket contains 4 flowers of Rose and 3 flowers of Mogara. One flower is thrown out from the basket and after that a second flower is selected. The probability that the second flower is Mogara is ......
A.\[\dfrac{2}{7}\]
B.\[\dfrac{5}{7}\]
C.\[\dfrac{3}{7}\]
D.\[\dfrac{1}{7}\]

Answer 1

Hint: In the above given problem, we are given a basket which has two kinds of flowers which are the flowers of Rose and Mogara. The number of rose flowers is 4 whereas the number of mogara flowers is 3. Hence, the total number of flowers in the given basket is 7. Then at random, a flower is thrown out of the basket which could either be a rose or a mogara flower. And then a second flower is selected randomly from the remaining flowers of the basket. We have to determine the probability of the second flower being a mogara.

Complete answer:
Given that, a basket contains 4 rose flowers and 3 mogara flowers.
Hence, the total number of flowers in the given basket is 7.
Now, using the rules of probability we can say that the probability of choosing a flower of rose at random from the given basket is,
\[ \Rightarrow \dfrac{4}{7}\]
Similarly, the probability of choosing a flower of mogara at random from the given basket is,
\[ \Rightarrow \dfrac{3}{7}\]
Now according to the given question, a random flower is thrown out of the basket.
That flower can either be a rose or mogara having probability of being the same as \[\dfrac{4}{7}\] and \[\dfrac{3}{7}\] respectively.
Now, if we chose a second flower at random, then the probability of the second flower being a rose or mogara is still \[\dfrac{4}{7}\] and \[\dfrac{3}{7}\] respectively, because we don’t know exactly about the kind of previously thrown flower.
Therefore, the probability of the second flower being a mogara is \[\dfrac{3}{7}\] .

Note:
Similarly, if all the 6 flowers out of the 7 are thrown out of the basket at random then the probability of the last flower being a rose or mogara is still the same i.e. \[\dfrac{4}{7}\] and \[\dfrac{3}{7}\] respectively. This happens so, because it still means the same as choosing one flower at random out of the seven flowers.