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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So,
Let x represent Joe's weight and y represent Jeff's weight.
"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250
We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250
Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250
We will use Elimination by Substitution.
2y - 20 + y + 10 = 250
Collect Like Terms.
3y - 10 = 250
Add 10 to both sides.
3y = 260
Divide both sides by 3.
Substitute again.
Multiply.
Subtract.
Check.
"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.
Let x represent Joe's weight and y represent Jeff's weight.
"Joe weighs 20 lbs. less than twice Jeff's weight."
x = 2y - 20
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
(y + 10) + x = 250
We now have our two open sentences.
x = 2y - 20
(y + 10) + x = 250
Get rid of parentheses.
x = 2y - 20
x + y + 10 = 250
We will use Elimination by Substitution.
2y - 20 + y + 10 = 250
Collect Like Terms.
3y - 10 = 250
Add 10 to both sides.
3y = 260
Divide both sides by 3.
Substitute again.
Multiply.
Subtract.
Check.
"Joe weighs 20 lbs. less than twice Jeff's weight."
Jeff's weight times two is 173 and one-third.
20 lbs. less than that is 153 and one-third lbs. Check.
"If Jeff would gain 10 lbs., then together they would weigh 250 lbs."
86 and two-thirds + 10 = 96 and two-thirds.
96 and two-thirds + 153 and one-third equals 250 lbs. Check.