CONDITIONAL PROBABILITY WORD PROBLEMS WORKSHEET

Worksheet given in this section will be much useful for the students who would like to practice word problems on conditional probability.   

Worksheet

(1)  Can two events be mutually exclusive and independent simultaneously?      Solution

(2)  If A and B are two events such that P(A U B) = 0.7, P(A n B) = 0.2, and P(B) = 0.5, then show that A and B are independent.      Solution

(3)  If A and B are two independent events such that P(A∪B) = 0.6, P(A) = 0.2, find P(B).    Solution

(4)  If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A / B) and P(A∪B) .      Solution

(5)  If for two events A and B, P(A) = 3/4, P(B) = 2/5 and AUB = S (sample space), find the conditional probability P(A/B)          Solution

(6)  A problem in Mathematics is given to three students whose chances of solving it are 1/3, 1/4 and 1/5 (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?    Solution

(7)  The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15.    

(i)  If the oil had to be changed, what is the probability that a new oil filter is needed?

(ii)  If a new oil filter is needed, what is the probability that the oil has to be changed?      Solution

(8)  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

(9)  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

(10)  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

(11)  A year is selected at random. What is the probability that (i) it contains 53 Sundays (ii) it is a leap year which contains 53 Sundays       Solution

(12)  Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?      Solution

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WORD PROBLEMS

HCF and LCM  word problems

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OTHER TOPICS 

Profit and loss shortcuts

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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