You visited us 1 times! Enjoying our articles? Unlock Full Access!

Event

When a fair d...

Question

When a fair die is thrown twice, let $(a, b)$ denote the outcome in which the first throw shows $a$ and the second throw shows $b .$ Consider the following events: $A = {(a, b) | a is odd}, B = {(a, b) | b is odd}$ and $C = {(a, b) | a + b is odd},$ then which of the following(s) is(are) correct?

P (A \cap B) = P (B \cap C)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

P (A \cap C) = P (B \cap C)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

P (A \cap B \cap C) = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

P (A) = P (B) = P (C)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $P (A) = P (B) = P (C)$
Number of elements in sample space $n (s) = 6 \times 6 = 36$
odd faces $= {1, 3, 5},$ even faces $= {2, 4, 6}$
So, number of elements in A, $n (A) =^{3} C_{1} \cdot^{6} C_{1} = 18; a is odd$
and $n (B) =^{6} C_{1} \cdot^{3} C_{1} = 18; b is odd$
when $a + b =$ odd , $i . e .$ one face is showing odd number and other face is showing even number or one face is showing even number and other face is showing odd number.
So, $n (C) =^{3} C_{1} \cdot^{3} C_{1} +^{3} C_{1} \cdot^{3} C_{1} = 18$
So, $P (A) = P (B) = P (C) = \frac{18}{36} = \frac{1}{2}$
Now, $n (A \cap B) =$ both faces showing odd $=^{3} C_{1} \cdot^{3} C_{1} = 9$
For $(B \cap C) :$
$i . e .$ $a$ (even) $+ b$ (odd)=odd,
$=^{3} C_{1} \cdot^{3} C_{1} = 9 = n (A \cap C)$
So, $P (A \cap B) = P (B \cap C) = P (A \cap C) = \frac{1}{4}$
For $A \cap B \cap C : i . e .$ $a$ (odd) $+ b$ (odd)=odd (not possible)
So, $P (A \cap B \cap C) = 0$

Suggest Corrections

Similar questions

Q. Assertion :A fair die is thrown twice. Let (a, b) denote the outcome in which the first throw shows a and the second shows b. Let A and B be the following two events.

A = {(a, b) | a is even}, {(a, b) | b is even}

C = {(a, b) | a+b is odd}

, then

P (A \cap B \cap C) = 1 / 8

Reason: If

D = {(a, b) | a+b is even}

, then

P (A \cap B \cap D | A \cup B) = 1 / 3

Q. An unbiased die is thrown twice. Let the even

A

^{'} o d d^{'}

number on the first throw and

B

the event

^{'} o d d

number on the second throw'. Check the independence of the events

A

and

B

Q. Let two fair six-faced dice

A

and

B

are thrown simultaneously. If

E_{1}

is the event that die

A

shows up four,

E_{2}

is the event that die

B

shows up two and

E_{3}

is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

Let two fair six-faced dice A and B be thrown simulatneously. If $E_{1}$ is the event that die A shows up four, $E_{2}$ is the event that die B shows up two and $E_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is/are true ?

Q. In a simultaneous throw of two dice, find P (A or B) if A denotes the event 'a total of 11 and B denotes the event an odd number on each die.

Join BYJU'S Learning Program

Explore more

Event

Standard XI Mathematics

Join BYJU'S Learning Program

When a fair die is thrown twice, let (a,b) denote the outcome in which the first throw shows a and the second throw shows b. Consider the following events: A={(a,b) | a is odd},B={(a,b) | b is odd} and C={(a,b) | a+b is odd}, then which of the following(s) is(are) correct?

When a fair die is thrown twice, let $(a, b)$ denote the outcome in which the first throw shows $a$ and the second throw shows $b .$ Consider the following events: $A = {(a, b) | a is odd}, B = {(a, b) | b is odd}$ and $C = {(a, b) | a + b is odd},$ then which of the following(s) is(are) correct?