Suppose a girl throws a die. If she gets 1 or 2 , she tosses a coin three times and notes the number of tails. If she gets 3 , 4 , 5 , or 6 , she tosses a coin once and notes whether a ‘head’ or ‘tail’ is obtained. If she obtained exactly one ‘tail’, what is the probability that she threw 3 , 4 , 5 , or 6 with the die ?

Let E 1 be the event that the girl gets 1 or 2 . Thus, P E 1 = 2 6 = 1 3 Let E 2 be the event that the girl gets 3 , 4 , 5 , or 6 . Then P E 2 = 4 6 = 2 3 Let A be the event that she obtained exactly one tail. If she tossed a coin 3 times and exactly 1 tail showed up, then the total number of favorable outcomes = { ( THH ) , ( HTH ) , ( HHT ) } = 3 Thus, P A ∣ E 1 = 3 8 If she tossed the coin only once and exactly 1 tail showed up, the total number of favorable outcomes = T = 1 . Thus, P A ∣ E 2 = 1 2 The probability that she threw 3 , 4 , 5 or 6 with the die, given that she got exactly one tail can be found as follows: Or in other words, we need to find P E 2 | A We can use the Baye's theorem, according to which P E 2 | A = P E 2 P A ∣ E 2 P E 1 P A ∣ E 1 + P E 2 P A ∣ E 2 = 1 2 · 2 3 1 2 · 2 3 + 3 8 · 1 3 = 1 3 1 3 + 1 8 = 8 11 Hence, the required probability is 8 11 .

MEDIUM

Earn 100

Which method of redemption requires the company to buy back its debentures in the open market?

50% studentsanswered this correctly

Important Questions on The d- and f-Block Elements

HARD

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

When photon of energy

4.0 e V

strikes the surface of a metal

A,

the ejected photoelectrons have maximum kinetic energy

T_{A} e V

and de-Broglie wavelength

λ_{A} .

The maximum kinetic energy of photoelectrons liberated from another metal

B

by photon of energy

4.50 e V

T_{B} = (T_{A} - 1.5) e V .

If the de-Broglie wavelength of these photoelectrons

λ_{B} = 2 λ_{A},

then the work function of metal

B

is:

EASY

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

There are two bags, I and II. Bag I contains

3

red and

5

black balls and Bag II contains

4

red and

3

black balls. One ball is transferred randomly from Bag I to Bag II and then a ball is drawn randomly from Bag II. If the ball so drawn is found to be black in colour, then find the probability that the transferred ball is also black.

MEDIUM

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

A man is known to speak 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.

MEDIUM

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

If the light of wavelength $412.5 nm$ is incident on each of the metals given below, which ones will show photoelectric emission and why?

Metal	Work Function(eV)
Na	1.92 eV
K	2.15 eV
Ca	3.20 eV
Mo	4.17 eV

EASY

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

What are the different oxidation states exhibited by lanthanoids?

MEDIUM

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

What is photoelectric effect?

MEDIUM

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

Of the students in a college, it is known that

60 %

reside in hostel and

40 %

are day scholars (not residing in hostel). Previous year results report that

30 %

of all students who reside in hostel attain

A

grade and

20 %

of day scholars attain

A

grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an

A

grade, what is the probability that the student is hostler?

EASY

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

What is work function?

MEDIUM

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

A bag contains

4

red and

6

black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

HARD

Chemistry>Inorganic Chemistry>The d- and f-Block Elements>General Properties of Lanthanoids

A manufacturer has three machine operators

A, B

and

C

. The first operator

A

produces

1 %

of defective items, whereas the other two operators

B

and

C

produces

5 %

and

7 %

defective items respectively.

A

is on the job for

50 %

of the time.

B

on the job

30 %

of the time and

C

on job for

20 %

of the time. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by