Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules: If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz. If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz. If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz. For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules:
- If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz.
- If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz.
- If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz.
For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite.
What is true about the fourth quiz? Choose one of the following:
1. 115 students favour WA; 52 students favour S; and 83 favour GG.
2. 113 students favour WA; 55 students favour S; and 82 favour GG.
3. 111 students favour WA; 55 students favour S; and 84 favour GG.
4. 120 students favour WA; 60 students favour S; and 70 favour GG.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
