Question

Simone and her three friends were deciding how to pick the song they will sing for their school’s talent show. They decide to roll a number cube. The person with the lowest number chooses the song. If her friends rolled a 6, 5 and 2, what is the probability that Simone will get to choose the song?
(a) \[\dfrac{1}{6}\]
(b) \[\dfrac{1}{3}\]
(c) 0
(d) 1

Answer 1

Hint: In this type of question we have to use the concept of probability. We know that, if all outcomes are equally likely then the probability of a simple event is a ratio that compares the number of favourable outcomes to the number of possible outcomes that is\[\text{Probability = }\dfrac{\text{Number of favourable outcomes}}{\text{Number of all possible outcomes}}\].

Complete step by step answer:
Now we have to find the probability that the Simone will get to choose song and provided that Simone and her three friends were deciding to pick the song they will sing for their school’s talent show for that they decide to roll a number cube, the person with the lowest number chooses the song and her friends rolled a 6, 5 and 2.
As Simone and her friends use a number cube, the possible outcomes of rolling a number cube are 1, 2, 3, 4, 5 and 6.
\[\Rightarrow \text{Number of all possible outcomes}=n\left( S \right)=6\]
In order for Simone to be able to choose the song, she will need to roll a 1 and this can be done in only one way.
\[\Rightarrow \text{Number of favourable outcomes}=1\]
Let us suppose that \[p\left( A \right)\] will denote the probability that Simone chooses the song.
\[\begin{align}
  & \Rightarrow p\left( A \right)=\dfrac{\text{Number of favourable outcomes}}{\text{Number of all possible outcomes}} \\
 & \Rightarrow p\left( A \right)=\dfrac{1}{6} \\
\end{align}\]
Hence, the probability that Simone will choose the song is \[\dfrac{1}{6}\].

So, the correct answer is “Option a”.

Note: In this type of question students have to note that as we are considering a number cube it has six faces and hence the possible outcomes are 1, 2, 3, 4, 5 and 6. Students have to note that the person with the lowest number chooses the song and Simone’s friends already rolled a 6, 5 and 2 so that Simone will get a chance only if she rolled 1. Also students have to remember the formula of probability.