Question

A CD player chooses a track from three discs each with 20 tracks. What is the probability that it chooses track 2 of disc 2?
$\left( A \right)$ 1/10
$\left( B \right)$ 2/45
$\left( C \right)$ 1/60
$\left( D \right)$ 1/30

Answer 1

Hint – In this particular question first calculate the total number of tracks then calculate the probability of choosing disk 2 and track 2 from disk 2 respectively later on in the solution multiplied these probabilities so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
There are 3 discs.
Each has 20 racks.
Now it is given that a CD player chooses a track at random from these three discs.
Now the total number of tracks = (20 + 20 + 20) = 60 racks.
Now we have to find the probability that a randomly chosen track is from disc 2 and track 2.
Now as we know that the probability is the ratio of the favorable number of outcomes to the total number of outcomes.
Therefore, P = $\dfrac{{{\text{favorable number of outcomes}}}}{{{\text{total number of outcomes}}}}$
Now as there are 3 disk available so the probability to select disk 2 out of three disks is
Favorable number of outcomes = disk 2 = 1
Total number of outcomes = total disks = 3
So the probability (P1) to select disk 2 out of three disks = ${P_1} = \dfrac{1}{3}$
Now as there are 20 tracks in this particular disk so the probability (P2) to select track 2 is
Favorable number of outcomes = track 2 = 1
Total number of outcomes = total tracks = 20
So the probability (P2) to select rack 2 out of 20 racks = ${P_2} = \dfrac{1}{{20}}$
Now the probability (P) that randomly chosen track is from disc 2 and track 2 is the multiplication of the above calculated probabilities so we have,
Therefore, P = ${P_1} \times {P_2}$
$\Rightarrow P = \dfrac{1}{3} \times \dfrac{1}{{20}} = \dfrac{1}{{60}}$
So this is the required probability.
Hence option (C) is the correct answer.

Note – Whenever we face such types of questions the key concept we have to remember is that probability is the ratio of the favorable number of outcomes to the total number of outcomes, so first calculate the probabilities of randomly chosen disk 2 and track 2 from disk 2 separately then to get the required probability that it chooses track 2 of disk 2 is the multiplication of the above calculated probabilities.