# CONDITIONAL PROBABILITY WORD PROBLEMS

## About "Conditional Probability Word Problems"

Conditional Probability Word Problems :

Here we are going to see some example problems on conditional probability.

Question 1 :

One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that (i) both are white (ii) both are black (iii) one white and one black

Solution :

Let "w" be the event of choosing white ball.

Let "B1" and "B2" be the events of choosing first and second bag respectively.

Bag 1 :

There are 5 white and 3 black balls.

Number of ball in bag 1  =  8

Probability of selecting white ball from bag 1

P(W/B1)  =  5C1/8C1  =  5/8   ----(1)

Bag 2 :

There are 4 white and 6 black balls.

Number of ball in bag 2  =  10

Probability of selecting white ball from bag 2

P(W/B2)  =  4C1/10C =  4/10   ----(2)

(1) ⋅ (2)

P(W/B1) ⋅  P(W/B2)  =  (5/8) ⋅ (4/10)

=  1/4

(ii) both are black

P(B/B1)  =  3C1/8C1  =  3/8   ----(3)

P(B/B2)  =  6C1/10C =  6/10   ----(4)

(3) ⋅ (4)

P(B/B1) ⋅  P(B/B2)  =  (3/8) ⋅ (6/10)

=  9/40

(iii) one white and one black

=  P(W/B1) ⋅ P(B/B2) + P(B/B1) ⋅ P(W/B2)

=  (5/8)(6/10) + (3/8)(4/10)

P(one white and one black)  =  21/40

Question 2 :

Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks

Solution :

P(boys)  =  2/3

P(Girls)  =  1/3

Let "A" be the event of getting first grade

P(Boy getting first grade)  =  P(A/B)  =  0.70 and

P(Girl getting first grade)   =  P(A/G)  =  0.85

P(Selecting a student getting first grade)

=  P(B) P(A/B) + P(G) P(A/G)

=  (2/3) (0.70) + (1/3) (0.85)

=  (140/300) + (85/300)

=  225/300

=  3/4

=  0.75

Question 3 :

Given P(A) = 0.4 and P(AUB) = 0.7. Find P(B) if (i) A and B are mutually exclusive (ii) A and B are independent events (iii) P(A / B) = 0.4 (iv) P(B / A) = 0.5

Solution :

(i) A and B are mutually exclusive

If A and B are mutually exclusive events, then P(AnB)  =  0

P(AUB)  =  P(A) + P(B) - P(AnB)

0.7  =  0.4 + P(B)

P(B)  =  0.7 - 0.4  =  0.3

(ii) A and B are independent events

P(AnB)  =  P(A) P(B)

P(AUB)  =  P(A) + P(B) - P(A) P(B)

0.7  =  0.4 + P(B) (1 - P(A))

0.7 - 0.4 =  P(B) (1 - 0.4)

0.3  = P(B) (0.6)

P(B)  =  0.3/0.6

=  0.5

(iii) P(A / B) = 0.4

P(A/B)  =  P(AnB)/P(B)

0.4  =  P(AnB)/P(B)

P(AnB)  =  0.4 P(B)  ----(1)

P(AUB)  =  P(A) + P(B) - P(AnB)

0.7  =  0.4 + P(B) - 0.4 P(B)

0.3  =  P(B)(1- 0.4)

0.3  =  P(B)(0.6)

P(B)  =  0.3/0.6  =  0.5

(iv) P(B/A) = 0.5

P(B/A)  =  P(AnB)/P(A)

0.5  =  P(AnB)/0.4

P(AnB)  =  0.2

P(AUB)  =  P(A) + P(B) - P(AnB)

0.7  =  0.4 + P(B) - 0.2

0.7  =  0.2  + P(B)

0.7 - 0.2 =  P(B)

P(B)  =  0.5

After having gone through the stuff given above, we hope that the students would have understood, "Conditional Probability Word Problems"

Apart from the stuff given in "Conditional Probability Word Problems", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6