Advance Math Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 2 EXERCISES
The following question based on Advance Math topic of quantitative aptitude
(a) ${11}/{45}$
(b) $7/{15}$
(c) ${14}/{45}$
(d) $9/{54}$
The correct answers to the above question in:
Answer: (b)
Required probability
= Probability that ball from bag A is red and both the balls from bag B are black + Probability that ball from bag A is black and one black and one red balls are drawn from bag
= ${^4C_1}/{^9C_1} × {^7C_2}/{^{10}C_2} + {^5C_1}/{^9C_1} × {^3C_1 × ^7C_1}/{^{10}C_2}$
= $4/9 × 7/{15} + 5/9 × 7/{15} = 7/{15}$
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Read more model questions set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
The probability of getting 10 in a single throw of three fair dice is :
a) $1/8$
b) $1/9$
c) $1/6$
d) $1/5$
Answer »Answer: (a)
Exhaustive no. of cases = $6^3$
10 can appear on three dice either as distinct number as following (1, 3, 6) ; (1, 4, 5); (2, 3, 5) and each can occur in 3! ways. Or 10 can appear on three dice as repeated digits as following (2, 2, 6), (2, 4, 4), (3, 3, 4) and each can occur in ${3!}/{2!}$ ways.
∴ No. of favourable cases = 3 × 3! + 3 × ${3!}/{2!}$ = 27
Hence, the required probability = ${27}/{6^3} = 1/8$
Question : 2
Ram and Shyam appear for an interview for two vacancies in an organisation for the same post. The probabilities of their selection are 1/6 and 2/5 respectively. What is the probability that none of them will be selected ?
a) $1/5$
b) $1/2$
c) $5/6$
d) $3/5$
Answer »Answer: (b)
Required probability = $(1 - 1/6) × (1- 2/5) = 5/6 × 3/5 = 1/2$
Question : 3
A car is parked by an owner amongst 25 cars in a row, not at either end. On his return he finds that exactly 15 places are still occupied. The probability that both the neighbouring places are empty is
a) ${15}/{184}$
b) ${15}/{92}$
c) ${91}/{276}$
d) None
Answer »Answer: (b)
Exhaustive number of cases = $^{24}C_{14}$
Favourable cases = $^{22}C_{14}$
Probability = ${^{22}C_{14}}/{^{24}C_14} = {15}/{92}$
Question : 4
In shuffling a pack of cards three are accidentally dropped. The probability that the missing cards are of distinct colours is
a) ${165}/{429}$
b) ${162}/{459}$
c) ${169}/{425}$
d) ${164}/{529}$
Answer »Answer: (c)
The first card can be one of the 4 colours, the second can be one of the three and the third can be one of the two. The required probability is therefore
4 × ${13}/{52} × 3 × {13}/{51} × 2 × {13}/{50} = {169}/{425}$.
Question : 5
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
a) 280
b) 196
c) 140
d) 346
Answer »Answer: (b)
The student can choose 4 questions from first 5 questions or he can also choose 5 questions from the first five questions.
∴ No. of choices available to the student
= $^5C_4 × ^8C_6 + ^5C_5 × ^8C_5$ = 196.
Question : 6
If the probability that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is
a) p + q – 2pq
b) p + q – pq
c) p + q
d) p + q + pq.
Answer »Answer: (a)
Only one of A and B can be alive in the following, mutually exclusive ways.
$E_1$ A will die and B will live
$E_2$ B will die and A will live
So, required probability = $P(E_1) + P (E_2)$
= p(1 - q) + q (1 - p) = p + q - 2pq.
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