Question

Eleven bags of wheat flour, each marked 5kgs, actually contained the following weights of flour (in kg):
\[4.97,{\text{ }}5.05,{\text{ }}5.08,{\text{ }}5.03,{\text{ }}5.00,{\text{ }}5.06,{\text{ }}5.08,{\text{ }}4.98,{\text{ }}5.04,{\text{ }}5.07,{\text{ }}5.00.\]
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Answer 1

Hint: Find the number of bags with weight higher than 5 kg and find the probability for it.
First, we find what is given, we are given 11 bags of wheat flour, it means that there total 11 possibilities and then calculate how many bags from the given 11 bags have weight more than 5 kgs. Then we use the probability formula and substitute according and get the required probability.

Complete step by step solution:
For probability to be calculated, we need to first find out the total possible events and also favourable outcomes out of the total outcomes.
First, we calculate the total outcomes, we are given a total of 10 bags, then it is clear that the total maximum outcomes are 10.
Now, coming to the favourable outcomes.
From the given 11 bags of wheat flour, we can see that there are 7 bags with weight above 5 kg, which are as following
\[{\text{ }}5.05,{\text{ }}5.08,{\text{ }}5.03,{\text{ }}5.06,{\text{ }}5.08,{\text{ }}5.04,{\text{ }}5.07,{\text{ }}\]
Hence, the favourable outcomes from the total outcomes are 7.
Now that we have favourable outcome and total outcomes, we can calculate the probability
The probability of an event = \[\dfrac{{favourable \;outcomes}}{{total \;outcomes}}\]

Probability of a bag contain more than 5 kilograms = \[\dfrac{{number{\text{ }}of{\text{ }}bags{\text{ }}with{\text{ }}weight{\text{ }}over{\text{ }}5{\text{ }}kg}}{{totalbags}}\]

Probability of a bag contain more than 5 kilograms= \[\dfrac{7}{{11}}\]

Note: We have to carefully notice what has been asked in the question, since we have been asked for a weight above 5 kg, we should not consider the bags with weight of exactly 5 kg. As it should be greater than 5 kg.