Question

There are two bags, A and B. A has 6 red flowers and 3 pink flowers. Bag B, on the other hand, contains two red flowers and seven pink flowers. One flower is drawn at random from a bag. What is the probability that the chosen flower is pink?

Answer 1

We must first determine the probability of selecting one bag and then the probability of selecting the second bag. The probability of finding the pink flower in one bag is then calculated. The chance of the pink flower in the second bag is then calculated. To calculate the probability of a pink flower being pulled, we use the conditional probability formula.

Complete step-by-step solution:
We are given 6 red and 3 pink flowers in bag A.
So, the total flowers in bag A = 6red+3pink =9 flowers
Similarly, total flowers in bag B =2 red+7 pink=9 flowers
We will now find the probability of choosing a pink flower from bag A.
Probability of finding a pink flower in bag A $= \dfrac{\text{number of pink flowers in bagA}}{\text{total number of flowers}}$
Probability of finding a pink flower in bag A $= \dfrac{3}{9}$
Similarly for bag B we will find the probability of choosing a pink flower from bag B.
Probability of finding a pink flower in bag B $= \dfrac{7}{9}$
We have total probability of choosing pink flower
$= \dfrac{3}{9} + \dfrac{7}{9}$
$= \dfrac{{10}}{9}$
We have only two bags
so, we will find the probability of selecting a bag $= \dfrac{1}{2}$
We can calculate the probability of choosing a pink flower by the product of the total probability of choosing a pink flower and the probability of selecting a bag.
So, the probability of choosing pink flower $= \dfrac{1}{2} \times \dfrac{{10}}{9}$
The probability of choosing a pink flower is $= \dfrac{5}{9}$.

Note: The use of the suitable probability approach is a critical step in this challenge. In such cases, we always start with conditional probability and then move on to the law of total probability. The Bayes theorem outlines the probability of an event occurring under any condition. It's also taken into account in the case of conditional probability. The Bayes theorem is sometimes known as the "causes" formula.