Introduction to 6th grade math 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 6th grade math probability:
Example: 1
Two dice are rolled. A is the event that the sum of the numbers shown on the two dice is 5, and B is the event that at least one of the dice shows up a 3. Are the two events
(i) Mutually exclusive
(ii) Exhaustive? Give the arguments in support of your answer.
Solution:
When two dice are rolled, we have n(s) = (6 x 6) = 36.
Now, A = {(1, 4), (2,3),(4,1),(3,2)} and
B = {(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6), (1,3), (2,3), (4,3), (5,3), (6,3)}
(i) A`nn`B = {(2,3), (3,2)} `!=` `phi` .
(ii) Also, A`uu`B `!=` s
Therefore A and B are not exhaustive events.
Example: 2
Two dices are rolled. Let A, B, C be the event getting a sum of 2, a sum of 3 and a sum of 4 respectively. Then, show that
(i) A is a simple event
(ii) B and C are compound events
(iii) A and B are mutually exclusive
Solution:
Clearly we have
A = {(1, 1), B = (1,2),(2,1) and c = (1,3),(3,1),(2,2)}
(i) Since A consists of a single sample point, it is a simple event.
(ii) Since both B and C contain more than one sample point, each one of them is compound event.
(iv) Since A`nn` B =`phi`, A and B are mutually exclusive.
Please express your views of this topic Rules of Probability by commenting on blog.
Practice problems for 6th grade math probability:
1. From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is
(i) red and a king
(ii) Either red or a king
[Answer: (i) 1/26
(ii) 7/13]
2.The odds in favour of occurrence of an event are 5:12. Find the probability of the event.
[Answer: 5/17]
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 6th grade math probability:
Example: 1
Two dice are rolled. A is the event that the sum of the numbers shown on the two dice is 5, and B is the event that at least one of the dice shows up a 3. Are the two events
(i) Mutually exclusive
(ii) Exhaustive? Give the arguments in support of your answer.
Solution:
When two dice are rolled, we have n(s) = (6 x 6) = 36.
Now, A = {(1, 4), (2,3),(4,1),(3,2)} and
B = {(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6), (1,3), (2,3), (4,3), (5,3), (6,3)}
(i) A`nn`B = {(2,3), (3,2)} `!=` `phi` .
(ii) Also, A`uu`B `!=` s
Therefore A and B are not exhaustive events.
Example: 2
Two dices are rolled. Let A, B, C be the event getting a sum of 2, a sum of 3 and a sum of 4 respectively. Then, show that
(i) A is a simple event
(ii) B and C are compound events
(iii) A and B are mutually exclusive
Solution:
Clearly we have
A = {(1, 1), B = (1,2),(2,1) and c = (1,3),(3,1),(2,2)}
(i) Since A consists of a single sample point, it is a simple event.
(ii) Since both B and C contain more than one sample point, each one of them is compound event.
(iv) Since A`nn` B =`phi`, A and B are mutually exclusive.
Please express your views of this topic Rules of Probability by commenting on blog.
Practice problems for 6th grade math probability:
1. From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is
(i) red and a king
(ii) Either red or a king
[Answer: (i) 1/26
(ii) 7/13]
2.The odds in favour of occurrence of an event are 5:12. Find the probability of the event.
[Answer: 5/17]
