Question

A box contains 20 packets of potato chips.
6 packets contain barbecue flavoured chips.
10 packets contain salt flavoured chips.
4 packets contain chicken flavoured chips.
Maria takes two packets at random without replacement.
Show that the probability that she takes two packets of salt flavoured chips is $\dfrac{9}{38}$.

Answer 1

Hint: Calculate the probability of selecting two packets of salt flavoured chips from the box in succession without replacement and then use fundamental principle of multiplication to calculate the required probability.

Complete step-by-step answer:
Total number of packets of potato chips in box = 20
Out of these, 10 packets contain salt flavoured chips.
From the box, Maria takes two packets at random without replacement.
Now, Probability of the first packet selected by Maria to be Salt flavoured is the number of salt flavoured packets divided by the total number of packets = $\dfrac{10}{20}$.
As she takes out packets without replacement so after taking out one packet from the box, the total packet left in the box is 19.
We have to find the probability of two packets taken out by maria to be salt flavoured. Thus, we assume that the first packet taken out by her contains salt flavoured chips.
Thus, the total salt flavoured chips packets left in the box is 10 – 1 = 9.
Now, Probability of the second packet taken out by Maria to be salt flavoured = $\dfrac{9}{19}$.
Since both the events of selecting first packet and then second happen at a single time, thus by multiplicative rule, required probability is given by $\dfrac{10}{20} \times \dfrac{9}{19}=\dfrac{9}{38}$.
Hence, the probability that she takes two packets of salt flavoured chips is $\dfrac{9}{38}$.

Note: In this type of questions, we use the concept of probability without replacement in which one item once drawn is not replaced back. So, we don’t replace the first packet chosen by us before we choose the second. After calculating individual probabilities for the 2 draws of packets (say m and n), we use the fundamental principle of multiplication to find the probability of two draws in succession ($m \times n$).