Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following event
s: A:{ The sum of the numbers is odd } B:{ The sum of the numbers is 10 or more } C:{ A 3 appears on each of the two dice }
1 answer:
Answer:
Step-by-step explanation:
The sample space is shown in the attached photo.
Probability = number of favourable outcomes/total number of outcomes.
Looking at the diagram, the total possible outcomes is 36.
A) from the diagram, the total number of events in which the sum of the numbers is odd is 18. Therefore, the probability that the sum of the numbers is odd is
18/36 = 1/2
B) the total number of events in which the sum of the numbers is 10 or more is 6. Therefore, the probability that the sum of the numbers is 10 or more is
6/36 = 1/6
C) the total number of events in which 3 appears on each of the two dice is 1. Therefore, the probability that 3 appears on each of the two dice is
1/36
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Answer:
Using a discrete probability distribution, it is found that:
a) There is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.
b) There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.
c) The expected value is of 1.3 lawns mowed on a randomly selected day.
<h3>What is the discrete probability distribution?</h3>Researching the problem on the internet, it is found that the distribution for the number of lawns mowed on a randomly selected dayis given by:
- P(X = 0) = 0.2.
- P(X = 1) = 0.4.
- P(X = 2) = 0.3.
- P(X = 3) = 0.1.
Item a:
P(X = 2) = 0.3, hence, there is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.
Item b:
There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.
Item c:
The expected value of a discrete distribution is given by the <u>sum of each value multiplied by it's respective probability</u>, hence:
E(X) = 0(0.2) + 1(0.4) + 2(0.3) + 3(0.1) = 1.3.
The expected value is of 1.3 lawns mowed on a randomly selected day.
More can be learned about discrete probability distributions at brainly.com/question/24855677