The sample space $S$ of a random experiment is given by $S = a_{1}, a_{2}, a_{3}, a_{4}$ with probabilities $P (a_{1}) = 0.3. P (a_{2}) = 0.1$ , $P (a_{3}) = 0.4$ and $P (a_{4}) = 0.2$ Consider events $A$ and $B$ as $A = a_{1}, a_{2}$ and $B = a_{2}, a_{3} a_{4}$ $P (A^{'} ⋂ B^{'}) =$

1

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

0.8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $1$
Given,
$S = a_{1}, a_{2} . a_{3}, a_{4}$

$P (a_{1}) = 0.3, P (a_{2}) = 0.1, P (a_{3}) = 0.4, P (a_{4}) = 0.2$

$P (A) = P (a_{1}) + P (a_{2}) = 0.3 + 0.1 = 0.4$

$P (B) = P (a_{3}) + P (a_{4}) = 0.4 + 0.2 = 0.6$

$P (A \cup B) = 1$

As we know that,

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

$⟹ 1 = 0.4 + 0.6 - P (A \cap B) ⟹ P (A \cap B) = 0$

$P (A^{'} \cap B^{'}) = 1 - P (A \cap B) = 1 - 0 = 1$

Hence $P (A^{'} \cap B^{'}) = 1$

Suggest Corrections

Similar questions

An urn contains fair tickets with numbers 112, 121, 211, 222 and one ticket is drawn. Let $A_{i}$ (i = 1,2,3) be the event that the i $^{t h}$ digit of the number of ticket drawn is 1 then

Q. If

a_{1}

a_{2}

a_{3}

a_{4}

and

b

are real numbers such that

(a_{1}^{2} + a_{2}^{2} + a_{3}^{2}) b^{2} - 2 (a_{1} a_{2} + a_{2} a_{3} + a_{3} a_{4}) b + (a_{2}^{2} + a_{3}^{2} + a_{4}^{2}) \leq 0

then

a_{1}

a_{2}

a_{3}

a_{4}

are the terms of a/an

Q. If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P(

A \cap B

) = 0.1, then of P(

A \cap B

) =_______________.

Q. If

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

then

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

Q. It is a KVPY question Let a1,a2,a3,a4 be real number such that a1+a2+a3+a4=0 and a1^2+a2^2+a3^2+a4^2=1 then the smallest possible value of the expression (a1-a2)^2+(a2-a3)^2+(a3-a4)^2+(a4-a1)^2 lies in which interval. Not sure about the chapter..

Join BYJU'S Learning Program

The sample space S of a random experiment is given by S=a1,a2,a3,a4 with probabilities P(a1)=0.3.P(a2)=0.1, P(a3)=0.4 and P(a4)=0.2 Consider events A and B as A=a1,a2 and B=a2,a3a4 P(A′⋂B′)=

The correct option is A 1Given,S=a1,a2.a3,a4P(a1)=0.3,P(a2)=0.1,P(a3)=0.4,P(a4)=0.2P(A)=P(a1)+P(a2)=0.3+0.1=0.4P(B)=P(a3)+P(a4)=0.4+0.2=0.6P(A∪B)=1As we know that,P(A∪B)=P(A)+P(B)−P(A∩B)⟹1=0.4+0.6−P(A∩B)⟹P(A∩B)=0P(A′∩B′)=1−P(A∩B)=1−0=1Hence P(A′∩B′)=1

The sample space $S$ of a random experiment is given by $S = a_{1}, a_{2}, a_{3}, a_{4}$ with probabilities $P (a_{1}) = 0.3. P (a_{2}) = 0.1$ , $P (a_{3}) = 0.4$ and $P (a_{4}) = 0.2$ Consider events $A$ and $B$ as $A = a_{1}, a_{2}$ and $B = a_{2}, a_{3} a_{4}$ $P (A^{'} ⋂ B^{'}) =$