Probability Math 7

Introduction to probability math for grade 7:

Probability is the method 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  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.

I like to share this Probability Math Problems with you all through my article.

Example problems for probability math 7:


Ex: 1    For two events A and B, P(A) = 0.5, P(B) = 0.6 and P(A `U ` B) = 0.8. Find the

(i) P(`A/B` )

(ii) P(`B/A` ).

Sol:   P(A) = 0.5,

P(B) = 0.6 and

P(A`uu` B) = 0.8

Now,

P(A`uu` B) = P(A) + P(B) –P(A`nn` B)

P(A`nn` B) = P(A) +P(B) –P(A `U` B)

= (0.5 + 0.6 – 0.8)

= 0.3

Thus, P(A`nn` B) = 0.3

Therefore (i) P(`A/B` ) =`(P(AnnB))/(P(B))` =`0.3/0.6` = `3/6` = `1/2 ` = 0.5

(ii) P(`B/A` ) =` (P(AnnB))/(P(A))` = `0.3/0.5` = `3/5` = 0.6

Hence, P(`A/B` ) = 0.5 and P(`B/A` ) = 0.6

Ex: 2    A die is rolled. If the outcome is an odd number, What is probability that it is prime?

Sol:   When a die is rolled, sample space is S = {1, 2, 3, 4, 5, 6}

Let A = Event of getting an odd number, and

B = Event of getting a prime number.

Then, A = {1, 3, 5}, B = {2, 3, 5} and A B ={3,5}.

Therefore  P(A) = `(n(A))/(n(S))` = `3/6` = `1/2`

P(B) = `(n(A))/(n(S))` = `3/6` = `1/2` and

P(A`nn` B) =` (n(AnnB))/(n(S))` = `2/6` = `1/3.`

Suppose A has already occurred and then B occurs.

Now, `P(B/A)` = `(P(AnnB))/(P(A))` = `(1/3) / (1/2)` = `(1/3 xx 2/1)` = `2/3.`

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Practice problems for probability math 7:


1. A die is rolled. If the outcome is an even number, What is the probability that it is a number greater than 2?

[Ans: `2/3` ]

2. A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die.

[Ans: `1/3` ]