PROBABILITY WORD PROBLEMS WORKSHEET USING ADDITION THEOREM

(1)  If P (A) = 2/3, P(B) = 2/5, P(AU B) = 1/3 then find P(AnB).          Solution 

(2)  A and B are two events such that, P(A) = 0.42, P(B) = 0.48 and P(A n B) = 0.16. Find

(i) P (not A) (ii) P (not B) (iii) P (A or B)         Solution 

(3)  If A and B are two mutually exclusive events of a random experiment and P(not A) = 0.45, P(A U B) = 0.65, then find P(B)          Solution 

(4)  The probability that at least one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find P(A bar) + P(B bar).         Solution 

(5)  The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then find the probability that neither A nor B happen

Solution 

(6)  Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.             Solution

(7)  From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of it being either a red king or a black queen.          Solution

(8)  A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.            Solution      

(9)  Three unbiased coins are tossed once. Find the probability of getting utmost 2 tails or at least 2 heads.

Solution

(10)  The probability that a person will get an electrification contract is 3/5 and the probability that he will not get plumbing contract is 5/8 . The probability of getting at least one contract is 5/7. What is the probability that he will get both?         Solution

(11)  In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?                Solution

(12)  A coin is tossed thrice. Find the probability of getting exactly two heads or at least one tail or consecutive two heads.            Solution

(13)  If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A n B) = 1/6, P(BnC) = 1/4, P(AnC) = 1/8, P(A U B U C) = 9/10, P(A n B n C) = 1/15, then find P(A), P(B) and P(C) ?       Solution

(14)  In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.       Solution

Problem 1 :

If A and B are mutually exclusive events P(A)  =  3/8 and P(B)  =  1/8, then find (i) P(A') (ii) P(A U B) (iii) P(A' n B) (iv) P(A' U B')

Solution

Problem 2 :

If A and B are two events associated with a random experiment for which P(A) = 0.35, P(A or B) = 0.85, and P(A and B) = 0.15. Find (i) P(only B) (ii) P(B') (iii) P(only A)

Solution

Problem 3 :

A die is thrown twice. Let A be the event, ‘First die shows 5’ and B be the event, ‘second die shows 5’. Find P(A∪B) .

Solution

Problem 1 :

Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.

Solution

Problem 2 :

From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of it being either a red king or a black queen.

Solution

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