Question

Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):
$4.97,5.05,5.08,5.03,5.00,5.06,5.08,4.98,5.04,5.07,5.00$
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
A.$\dfrac{7}{{11}}$
B.$\dfrac{8}{{11}}$
C.$\dfrac{9}{{11}}$
D.None of the above

Answer 1

Hint: Here, we are required to find the probability that any of the given bags chosen at random contains more than 5 kg of flour. We know that there are 11 bags of wheat. Hence, this will be our total outcomes. We will observe the given weights of flour and count the number of favorable outcomes i.e. the number of bags containing more than 5 kg of flour. Dividing the favorable outcomes by the total outcomes, we will get the required probability.
Formula Used:
Probability, $P = $Number of favorable outcomes$ \div $Total number of outcomes

Complete step-by-step answer:
According to the question,
Total number of bags $ = 11$
Now, it is given that each bag is marked 5 kg, but actually they contained the following weights of flour (in kg):
$4.97,5.05,5.08,5.03,5.00,5.06,5.08,4.98,5.04,5.07,5.00$
Here, we can observe that:
The bags having less than 5 kg of flour $ = \left\{ {4.97,4.98} \right\} = 2$ bags
The bags having exactly 5 kg of flour $ = \left\{ {5.00,5.00} \right\} = 2$ bags
The bags having more than 5 kg of flour $ = \left\{ {5.05,5.08,5.03,5.06,5.08,5.04,5.07} \right\} = 7$ bags
Now, according to the question, we are required to find the probability that any of these bags chosen at random contains more than 5 kg of flour.
We know that Probability, $P = $ Number of favorable outcomes $ \div $Total number of outcomes
In this question,
Total number of outcomes $ = $ Total number of bags $ = 11$
Also, number of favorable outcomes $ = $ the bag chosen at random contains more than 5 kg of flour\[ = 7\]
Therefore, required probability, $P = \dfrac{7}{{11}}$
Hence, the probability that any of these bags chosen at random contains more than 5 kg of flour$ = \dfrac{7}{{11}}$
Therefore, option A is the correct answer.


Note: Probability tells us the extent to which an event is likely to occur, i.e. the possibility of the occurrence of an event. Hence, it is measured by dividing the favorable outcomes by the total number of outcomes. It is used by meteorologists as it helps them to use the weather patterns and predict the probability of rain. Also, we use probability in our day to day life to make decisions when we are not sure about the result of that decision. Hence, this concept is important in our everyday life as well.