40
Q:

# 8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :

 A) 8/39 B) 15/39 C) 12/13 D) None of these

Explanation:

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)

= $\inline 1-\left ( \frac{^{16}\textrm{C}_{1}\times^{14}\textrm{C}_{1}\times ^{12}\textrm{C}_{1}\times ^{10}\textrm{C}_{1} }{^{16}\textrm{C}_{4}} \right )=\frac{15}{39}$

Q:

The Manager of a company accepts only one employees leave request for a particular day. If five employees namely Roshan, Mahesh, Sripad, Laxmipriya and Shreyan applied for the leave on the occasion of Diwali. What is the probability that Laxmi priya’s leave request will be approved ?

 A) 1 B) 1/5 C) 5 D) 4/5

Explanation:

Number of applicants = 5
On a day, only 1 leave is approved.
Now favourable events =  1 of 5 applicants is approved
Probability that Laxmi priya's leave is granted = 1/5.

4 28
Q:

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?

 A) 6/19 B) 3/10 C) 7/10 D) 6/17

Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20
Let E = event of getting a multiple of 4 or 15
=multiples od 4 are {4, 8, 12, 16, 20}
And multiples of 15 means multiples of 3 and 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.
= the common multiple is only (15).
=> E = n(E)= 6
Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.

5 68
Q:

Out of sixty students, there are 14 who are taking Economics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class ?

 A) 8/15 B) 7/15 C) 1/15 D) 4/15

Explanation:

Given total students in the class = 60
Students who are taking Economics = 24 and
Students who are taking Calculus = 32
Students who are taking both subjects = 60-(24 + 32) = 60 - 56 = 4
Students who are taking calculus only = 32 - 4 = 28
probability that a randomly chosen student from this group is taking only the Calculus class = 28/60 = 7/15.

7 88
Q:

Three unbiased coins are tossed. What is the probability of getting at most two heads ?

 A) 4/3 B) 2/3 C) 3/2 D) 3/4

Explanation:

Let S be the sample space.
Here n(S)= $\inline \fn_jvn \small 2^{3}$= 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.

4 143
Q:

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

 A) 2/3 B) 1/2 C) 7/8 D) 4/5

$\fn_jvn&space;\small&space;\therefore$ Required probability = 10/20 = 1/2.