Introduction to Probability

Q.

Three boys and four girls stand in queue for an interview. The probability that they stand in alternate positions is:

1. (1/35)

2. (3/35)

3. (1/49)

4. (3/49)

5. None of these

Q. The probability that man will be alive in $40$ years is $\frac{3}{5}$, and probability that his wife will also survive $40$ years is $\frac{2}{3}$. Find the probability that at least one will be alive.

1. $\frac{3}{5}$
2. $\frac{1}{2}$
3. $\frac{4}{15}$
4. $\frac{13}{15}$

Q. A man speaks truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

1. 
2. 
3. 
4. 

Q. A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold

1. 
2. 
3. 
4. 

Q.

Karan speaks the truth in 75% of cases and Sarosh in 80% of cases. In what percentage of cases are they likely to contradict each other in narrating the same event?

1. 65

2. 35

3. 5

4. None of these

5. 25

Q.

The following table shows the number of books in each shelf of different languages in a library. Study the table and answer what is the difference between the least number of language books and highest number of language books in the library?

Shelf Numbers	Malay	Chinese	English	Tamil
$1$	$73$	$112$	$158$	$64$
$2$	$83$	$100$	$102$	$49$
$3$	$56$	$92$	$75$	$54$
$4$	$66$	$138$	$175$	$59$

Q. A speaks truth in $60$% of the cases and B in $90$% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact$?$

Q.

Two toys are drawn from a bag containing 21 toys numbered from 1 to 21 (without replacement). Find the probability that both the toys will show even numbers.

1. 5/14

2. 9/14

3. 11/14

4. 3/14

5. None of these