Dear Reader, Below are four simple probability based questions that will help you to prepare for Wipro and other prominent company papers.
Question 1
There are nine different toppings in Merry Brown Pizza shop. They have to make pizzas with different toppings. In how many ways can the shop keeper make pizzas with 2 different toppings?
a) 36 b) 48 c) 72 d) none of these.
Answer : a) 36
Solution :
The question deals with choosing 2 toppings from 9 available toppings REGARDLESS of the ORDER in which we pick. In cases, where the order of choice doesn't matter we need to use Combination Formula of nCr (formula to choose r options from n available options regardless of order).
Number of ways to choose 2 different toppings from available 9 toppings = nCr = 9C2 = 9 X 8 / 1 x 2 = 36
Question 2
In a toy shop there are seven different varieties of toys. The shopkeeper wants to make a selection of different toys of 3 different varieties?
a) 28 b) 35 c) 56 d) none of these.
Answer : b) 35
Solution :
This question is similar to the 1st question.
Number of ways to select 3 varieties from 7 available varieties = nCr = 7C3 = 7 x 6 x 5 / 1 x 2 x 3 = 35
Question 3
In how many different ways can a group of 4 boys and 2 girls be made out of a total of 8 boys and 4 girls?
a) 240 b) 360 c) 280 d) 420
Answer : d) 420
Solution :
N1 = Number of ways to choose 4 boys from 8 boys = nCr = 8C4
N2 = Number of ways to choose 2 girls from 4 girls = nCr = 4C2
Number of ways to choose 4 boys and 2 girls out of a total of 8 boys and 4 girls = N1 X N2 = 8C4 x 4C2 = 70 x 6 = 420
Question 4
A typist was appointed in Correct technology services and she was asked to prepare 23 letters addressed to different people and prepare 23 covers addressed to them. She inserts these letters at random into the envelopes. (one letter per envelope). What is the probability that exactly one letter is inserted to the wrong envelope?
a) 7/23 b) 9/23 c) 0 d) 11/23
Answer : c) 0.
Solution :
There are 23 letters and 23 covers with addresses.
By mistake if the typist puts one of the letters in wrong address, there is no way but another letter has to be put in wrong cover. Hence, there is NO CHANCE that ONLY ONE of the letter is inserted in wrong envelope. Hence probability of such occurrence is 0.
For example, let the letters be L1, L2, L3..... L23 and let the respective covers with addresses be C1,C2,C3..... C23.
Lets say, if L2 is placed in C4 instead of C2 then L4 has left with no option but to be placed in C2. Hence, if one letter is misplaced, another letter has to be misplaced. Hence probability of ONLY ONE misplacement is zero as chances of ONLY ONE misplacement is zero.