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# eLitmus Probability questions for eLitmus exam | eLitmus Questions for pH Test

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 1 What is the probability of getting at least one six in a single throw of three unbiased dice ? A. 31/216 B. 91/216 C. 125/216 D. 81/216
See Answer & Explanation Lets Discuss
Correct answer is : B
Explanation

Three cases arise:

Case 1: When only one dice shows up a six

This dice can be any of the 1st, 2nd or 3rd dice. Find the probability for these three independent events and add them up to get the total probability

Probability that only 1st dice shows up a six: (probability that first dice shows up a 6) and (probability that second dice shows up other than 6) and (probability that third dice shows up other than 6)

=(1/6)*(5/6)*(5/6)

=25/216

similarly probability that 2nd dice shows up a six: (5/6)*(1/6)*(5/6) = 25/216

And, probability that 3rd dice shows up a six: (5/6)*(5/6)*(1/6) = 25/216

So probability that only one dice shows up a six: (25/216)+(25/216) +(25/216) = 75/216

Case 2:When two dice show up a six

Total number of ways of selecting a pair of dice that show up a six from a set of 3 dice are: 3C2=3

Find the probability of getting six on a pair of dice and multiply it by total number of such possible pairs

Probability of getting a six on a pair of dice = (1/6)*(1/6)*(5/6) = 5/216

So, total probability = 3*(5/216) = 15/216

Case 3: When all dice show up a six

In this case total probability is just (1/6)*(1/6)*(1/6) = 1/216

So total probability of getting at least one six = (75/216) + (15/216) + (1/216) = 91/216

 2 What is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? A. 1/15 B. 2/15 C. 4/15 D. 7/15
See Answer & Explanation Lets Discuss
Correct answer is : C
Explanation

Since every third number starting from 10 will be divisible by 3, so total number of numbers divisible by 3 are 90/3 = 30

Numbers which are divisible by 3 and 5 both are numbers which are multiple of 15.

For the range 10 to 99, 15 is the first number divisible by 15 and 90 is the last number.

So total number of numbers divisible by 15 are: (90-15)/15 + 1 = 5 + 1 = 6

Number of numbers which are divisible by 3 are 30 and number of numbers which are divisible by 3 and 5 both are 6. So number of numbers divisible by 3 and not by 5 are: 30-6=24

So total probability = 24/90 = 4/15

 3 Out of 40 consecutive integers, two are chosen at random. Find the probability that their sum is odd? A. 21/40 B. 19/39 C. 21/39 D. 20/39
See Answer & Explanation Lets Discuss
Correct answer is : D
Explanation

Forty consecutive integers will have 20 even and 20 odd integers. The sum of 2 chosen integers will be odd, only if:

• First is even and second is odd
• First is odd and second is even
Mathematically the probability will be given by:
P(First is even) * P(Second is odd) + P(First is odd) + P(Second is even)

= (20/40) * (20/39) + (20/40) * (20/39)

= 20/39

 4 8 coins are tossed. Whats is the probability that one and only one turns up head ? A. 1/256 B. 1/32 C. 1/64 D. 1/128
See Answer & Explanation Lets Discuss
Correct answer is : B
Explanation

The coin that turns up head can be any of the eight.

Required probability = 8  * (1/28)

= 1/32

 5 A fair coin is tossed repeatedly. If head appears on first 5 tosses what is the probability that tail appears on 6th toss ? A. 1/6 B. 1/5 C. 1/3 D. 1/2
See Answer & Explanation Lets Discuss
Correct answer is : D
Explanation

Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on 6th toss is still 1/2.

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## eLitmus Probability Aptitude Objective Questions and Answers with Explanation

eLitmus Probability Aptitude Objective Questions and Answers for Government Sector job preparation. eLitmus Probability Aptitude Multiple Choice Questions are very important for exams like CAT,MAT,XAT, SSC IBPS, Bank PO, BPSC, UPSC, Govt Jobs, Bank Clerk , UPPSC etc.

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