Question

If the die is rolled 300 times, how many times would you predict a roll of a 1 or a 6.

Answer 1

Hint: Assume the event of rolling a dice 1 time as ‘S’ and the number of observations as n (S). Now, assume the event of getting a 1 or a 6 as ‘E’ and the number of these favorable outcomes as n (E). Find the probability of getting a 1 or a 6 by using the formula: - \[P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}\], where P (E) is the required probability. Once P (E) is found, multiply it with 300 to get the predicted number of a roll of a 1 or a 6.

Complete step by step answer:
Here, we are provided with the information that a die is rolled 300 times and we have been asked to predict the number of rolls of a 1 or a 6. To solve this question first we need to find the probability of getting a 1 or a 6 when the die is rolled one time.
Now, we know that a die is cubical in shape and has six faces on which numbers are marked from 1 to 6. So, let us consider the event of rolling the die 1 time as ‘S’ and the number of observations that can be obtained as n (S). Considering the event of getting a 1 or a 6 as ‘E’ and the number of these favorable outcomes as n (E), we have,
\[\Rightarrow \] n (S) = 6 and n (E) = 2
We know that probability of an event to occur is given as: - \[P\left( E \right)=\dfrac{n\left( E \right)}{n\left( S \right)}\], so we have,
\[\Rightarrow \] Probability of getting a 1 or a 6 when the die is rolled 1 time = \[\dfrac{2}{6}=\dfrac{1}{3}\].
Now, the predicted number of any event to occur is the product of the number of times the event is performed and the probability of the event to occur 1 time. So, we have,
Number of times the die is rolled = 300
Probability of getting a 1 or a 6 = \[\dfrac{1}{3}\]
\[\Rightarrow \] Predicted number of rolls of a 1 or a 6 = \[\dfrac{1}{3}\times 300=100\].
Hence, the number of times we would predict the roll of a 1 or a 6 is 100.

Note:
One may note that we do not have to find the probability of getting a 1 or a 6 for these 300 rolls of the dice but we just have to predict the number of rolls. So, do not get confused in these terms and remember the formula to calculate the predicted number of any event to occur. You must remember the formula to calculate the probability of an event to occur and always remember that \[P\left( E \right)\le 1\].