Math Word Problems Grade 9

Introduction to math word problem grade 9:

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented  group G is the algorithmic problem of deciding whether two words represent the same element. Although it is common to speak of the word problem for the group G strictly speaking it is a presentation of the group that does or does not have solvable word problem. (Source: Wikipedia)

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Example problems for math word problems grade 9:


Math word problems grade 9 – Example: 1

In the box 12 cards are placed as 1 to 12, mixed up thoroughly and  then a card is drawn at random from the box. if it is known that the number on the card is more than 3, find the probability that it is an even number.

Solution:

Let S be the sample space. then,

S = {1, 2, 3, 4, ......10, 11, 12}

Let A = Event of getting a card having a number more than 3.

And B = Event of getting a card having an even number.

Then, A = {4,5,6,7,8,9,10,11,12} and B = {2,4,6,8,10,12}

Therefore A B ={4,6,8,10,12}.

Therefore P(A) = `(n(A))/(n(S))` = `9/12` = `3/4`

P(B) = `(n(B))/(n(S))` = `6/12` = `1/12`

and P(A`nn` B) =`(P(AnnB))/(n(S))` = `5/12`

Suppose A has already occured and then B occurs.

Then, We have to find P(`B/A` )

Therefore P(`B/A` ) = P(A`nn` B) = `(P(AnnB))/(P(A))` = `(5/12)/(3/4)` = `(5/12 * 4/3)` = `5/9`

Math word problems grade 9 – Example: 2

The odds in favor of occurrence of an event 5:13. Find the odds against the occurrence of the event. Find the probability that it will occur.

Solution:

Odds in favor = `5/13`

Therefore Odds against = `13/5`

Number of favorable outcomes = 5

Number of unfavorable outcomes = 5 + 13

Required probability = `5/18`

Math word problems grade 9 – Example: 3

One card is drawn from a well shuffled deck of cards. Find the probability that the card is red ace.

Solution:

The number of possible outcomes n(s) = 52

Let A: getting a red ace card.

There are 2 red ace cards in the deck of the  cards n(A)  = 2.

P(ace) = P(A) = `(n(A))/(n(S))`

= `2/52`

= `1/26`

Math word problems grade 9 – Example: 4

A pair of dice is thrown. Find the probability of getting a doublet.

Solution:

When two dice are thrown, there are 36 sample points  n(S) = 36

A = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

n(A) = 6

P(a doublet) = `(n(A))/(n(S))`

= `6/36`

= `1/6`

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Practice problems for math word problems grade 9:


1. A, B and C shoot to hit a target. If A hits the target 4 times in 5 trials; B hits it 3 times in 4 trials and C hits it 2 times in 3 trials, what is the probability that the target is hit by at least 2 persons?

[Answer: The required probability is 5/6]

2.A card is drawn from a well-shuffled deck of 52 cards and without replacing this card, a second card is drawn. Find the probability that the first card is a club and the second card is spade.

[Answer: `13/204` ]