Answer:
A) 0.1612
B) 0.8031
C) 0.1969
Step-by-step explanation:
For each toss of the die, there are only two possible outcomes. Either it is a 3, or it is not. The probability of getting a 3 on each toss is independent from other tosses. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
Five tosses, so
The die has 6 values, from 1 to 6. The die is fair, so each outcome is equally as likely. The probability of a 3 appearing in a single throw is
(a) twice
This is
(b) at most once
(c) at least two times.
Either a 3 appears at most once, or it does at least two times. The sum of the probabilities of these events is decimal 1. So
We want
So