Introduction to Six Grade Probability:
Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
(Source: Wikipedia)
Example Problems for Six Grade Probability:
Six grade probability – Example: 1
Two coins are tossed. Find the probability of getting two heads.
Solution:
Step 1:
n (s) = {HH, HT, TH, TT}= 4
Step 2:
Tossing a coin with two heads:
n (a) = {HH}= 1
Step 3:
Formula:
P (A) = n(a)/n(s)
Answer:
P (A) = 1/4
Six grade probability – Example: 2
Three coins are tossed. Find the probability of getting two tails.
Solution:
Step 1:
n(s) = {TTT, TTH, THT, THH, HTT, HTH,HHT,HHH }= 8
Step 2:
There are 3 tosses with only two tails:
n (a) = { TTT, TTH, THT, HTT}=4
Step 3:
Formula:
P (A) = n(a)/n(s)
Answer:
P (A) = 4/8
P(A) = 1/2.
Six grade probability - Example: 3
When the die is rolled. What is the probability of occurring five?
Solution:
Total Number of possible = n (s) = {1, 2, 3, 4, 5, 6}
n (s) = 6
The number of outcomes n (a) = {5}
n (a) = 1
Formula:
P (A) = n(a)/n(s)
Therefore the probability of getting value = 1/6.
Six grade probability – Example: 4
When the two dice are rolled. What is the probability of occurring four or four?
Solution:
Total Number of possible = n (a) = { 1,1}{1,2}{1,3}{1,4}{1,5}{1,6}
{2,1}{2,2}{2,3}{2,4}{2,5}{2,6}
{3,1}{3,2}{3,3}{3,4}{3,5}{3,6}
{4,1}{4,2}{4,3}{4,4}{4,5}{4,6}
{5,1}{5,2}{5,3}{5,4}{5,5}{5,6}
{6,1}{6,2}{6,3}{6,4}{6,5}{6,6}
n (s) = 36
The number of outcomes n (a) = {1,4}{2,4}{3,4}{4,1}{4,2}{4,3}{4,4}
{4, 5}{4, 6}{5, 4}{6, 4}
n (a) = 11
Formula:
P (A) = n(a)/n(s)
Therefore the probability of getting value = 11/36. I have recently faced lot of problem while learning what is an acute angle, But thank to online resources of math which helped me to learn myself easily on net.
Practice Problems for Six Grade Probability:
1. Three coins are tossed and find the probability of all heads.
[Answer: P(A) = (1)/(8)]
2. Two dice are rolled then What is the probability of occurring six or six?
[Answer: (11)/(36)]
Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
(Source: Wikipedia)
Example Problems for Six Grade Probability:
Six grade probability – Example: 1
Two coins are tossed. Find the probability of getting two heads.
Solution:
Step 1:
n (s) = {HH, HT, TH, TT}= 4
Step 2:
Tossing a coin with two heads:
n (a) = {HH}= 1
Step 3:
Formula:
P (A) = n(a)/n(s)
Answer:
P (A) = 1/4
Six grade probability – Example: 2
Three coins are tossed. Find the probability of getting two tails.
Solution:
Step 1:
n(s) = {TTT, TTH, THT, THH, HTT, HTH,HHT,HHH }= 8
Step 2:
There are 3 tosses with only two tails:
n (a) = { TTT, TTH, THT, HTT}=4
Step 3:
Formula:
P (A) = n(a)/n(s)
Answer:
P (A) = 4/8
P(A) = 1/2.
Six grade probability - Example: 3
When the die is rolled. What is the probability of occurring five?
Solution:
Total Number of possible = n (s) = {1, 2, 3, 4, 5, 6}
n (s) = 6
The number of outcomes n (a) = {5}
n (a) = 1
Formula:
P (A) = n(a)/n(s)
Therefore the probability of getting value = 1/6.
Six grade probability – Example: 4
When the two dice are rolled. What is the probability of occurring four or four?
Solution:
Total Number of possible = n (a) = { 1,1}{1,2}{1,3}{1,4}{1,5}{1,6}
{2,1}{2,2}{2,3}{2,4}{2,5}{2,6}
{3,1}{3,2}{3,3}{3,4}{3,5}{3,6}
{4,1}{4,2}{4,3}{4,4}{4,5}{4,6}
{5,1}{5,2}{5,3}{5,4}{5,5}{5,6}
{6,1}{6,2}{6,3}{6,4}{6,5}{6,6}
n (s) = 36
The number of outcomes n (a) = {1,4}{2,4}{3,4}{4,1}{4,2}{4,3}{4,4}
{4, 5}{4, 6}{5, 4}{6, 4}
n (a) = 11
Formula:
P (A) = n(a)/n(s)
Therefore the probability of getting value = 11/36. I have recently faced lot of problem while learning what is an acute angle, But thank to online resources of math which helped me to learn myself easily on net.
Practice Problems for Six Grade Probability:
1. Three coins are tossed and find the probability of all heads.
[Answer: P(A) = (1)/(8)]
2. Two dice are rolled then What is the probability of occurring six or six?
[Answer: (11)/(36)]
