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If The Probability Of A To Fail In An Examination Is 02 And That For B Is 03 Then Probability That Either A Or B Is Fail Is

1) 0.5 2) 0.44 3) 0.8 4) 0.25 Solution: Option (2) 0.44 The probability that A fails in an exam = 0.2 The probability that B fails in an... View Article

The Probability That In The Toss Of Two Dice We Obtain The Sum 7 Or 11 Is

1) 1/6 2) 1/18 3) 2/9 4) 23/108 Solution: Option (3) 2/9 The total number of sample space, if two dice are tossed = 36 ways Let A be the... View Article

If Pb Equals 3by4 Pa Intersection B Intersection C 1by3 And Pa Intersection B Intersection C Equals 1by3 Then Pb Intersection C Is Equal To

1) 1/12 2) 1/6 3) 1/15 4) 1/9 Solution: Option (1) 1/12 Given that, P(B) = ¾, P(A∩B∩C’)= ⅓ and P(A’∩B∩C’)= ⅓ P(B∩C) = P(B)- [P(A∩B∩C’)+... View Article

A Bag Contains 3 Black 3 White And 2 Red Balls One By One Three Balls Are Drawn Without Replacement The Probability That The Third Ball Is Red Is

1) 2/56 2) 3/56 3) 1/56 4) 12/56 5) 14/56 Solution: Option (5) 14/56 Total number of balls = 8 Let W be the white ball, R be the red ball... View Article

An Antiaircraft Gun Can Take A Maximum Of Four Shots At Any Plane Moving Away From It The Probabilities Of Hitting The Plane At The

1) 0.6976 2) 0.3024 3) 0.72 4) 0.6431 5) 0.7391 Solution: Option (1) 0.6976 The probability that the gun hits the plane at 1st shot = 0.4 =... View Article

X Speaks Truth In 60 And Y In 50 Of The Cases The Probability That They Contradict Each Other Narrating The Same Incident Is

1) 1/4 2) 1/3 3) 1/2 4) ⅔ Solution: Option (3) ½ Given that probability that X speaks truth = 60% = 3/5 . Probability that Y speaks truth =... View Article

If A And B Are Mutually Exclusive With Pa Equals 1by2 Times Pb And A Union B Equals S Total Sample Space Then Pa Is Equal To

1) 2/3 2) 1/3 3) 1/4 4) ¾ Solution: Option (2) ⅓ Given that, P(A) = (1/2) × P(B) P(B) = 2P(A) A ∪ B = S Thus, P(AUB) = P(S) =1 As A and... View Article

Seven Chits Are Numbered 1 To 7 Four Chits Are Drawn One By One With Replacement The Probability That The Least Number Appearing On

1) (3/7)4 2) (6/7)3 3) (5. 4. 3)/73 4) (¾)3 Solution: Option (1) (3/7)4 Total number of cases = 7C1. 7C1 . 7C1 . 7C1 The... View Article

If A And B Are Mutually Exclusive Events With Pb Not Equal1 The Pa By B Is Equal To Here B Bar Is The Complement Of The Event B

1) 1/P(B) 2) 1/(1-P(B)) 3) P(A)/P(B) 4) P(A) / (1-P(B)) Solution: Option (4) P(A) / (1-P(B)) Given that A and B are mutually exclusive... View Article

The Probability That Atleast One Of The Events A And B Occurs Is 06 If A And B Occur Simultaneously With Probability 02 Then Pa Plus Pb Is Equal

1) 0.4 2) 0.8 3) 1.2 4) 1.4 Solution: Option (3) 1.2 Given that, P(AUB) = 0.6, P(A ∩ B) = 0.2 We have to find P(A’) + P(B’) We know that... View Article

An Urn Contains 3 Red And 5 Blue Balls The Probability That Two Balls Are Drawn In Which 2nd Ball Drawn Is Blue Without Replacement Is

1) 5/16 2) 5/56 3) 5/8 4) 20/56 Solution: Option (3) ⅝ Total number of balls = 3+5 = 8 balls Required Probability = P(First ball is red,... View Article

If Pa Equals Pb Equals X And Pa Intersection B Equals Pa Intersection B Equals 1by3 Then X Is Equal To

1) 1/2 2) 1/3 3) 1/4 4) ⅙ Solution: Option (1) ½ Given that, P(A) = P(B) = x P(A ∩ B) = P(A' ∩ B') = ⅓ P(A' ∩ B') = ⅓ P(A' ∩ B') can be... View Article

If Pa Equals 1by12 Pb Equals 5by12 And Pba Equals 1by15 Then Pa Union B Is Equal To

1) 89/180 2) 90/180 3) 91/180 4) 92/180 Solution: Option (1) 89/180 Given that, P(A) = 1/12, P(B) = 5/12 and P(B/A) = 1/15 We know that... View Article

Two Aeroplanes I And Ii Bomb A Target In Succession The Probabilities Of I And Ii Scoring A Hit Correctly Are 03 And 02 Respectively The Second

1) 0.06 2) 0.14 3) 0.32 4) 0.7 Solution: Option (3) 0.32 Let A be the event that Ist airplane hit the target and B be the event that IInd... View Article

One Indian And Four American Men And Their Wives Are To Be Seated Randomly Around A Circular Table Then The Conditional Probability That The

1) 1/2 2) 1/3 3) 2/5 4) ⅕ Solution: Option (c) ⅖ Let A be the event when Indian man is seated adjacent to his wife E be the event when each... View Article

If A And B Are Two Independent Events Such That Pb Equals 2 By 7 Pa Union B Equals 08 Then Pa Is Equal To

1) 0.1 2) 0.2 3) 0.3 4) 0.4 Solution: Option (3) 0.3 P(A ∪ B’) = P(A) + P(B’) - P(A∩B’) …(1) Note that: P(A∩B’) = P(A)- P(A∩B) Now,... View Article

If E1 And E2 Are Two Mutually Exclusive Events Of An Experiment With P Not E2 Equals 06 Equals Pe1 Union E2 Then Pe1 Is Equal To

1) 0.1 2) 0.3 3) 0.4 4) 0.2 Solution: Option (4) 0.2 Given that A and B are mutually exclusive events Hence, P(E1∩E2) = 0 Given: P(not E2)... View Article

For K Equals 1 2 3 The Box Bk Contains K Red Balls And K Plus 1 White Balls Let Pb1 Equals 1 By 2 Pb2 Equals 1 By 3 And Pb3 Equals 1 By 6

1) 35/78 2) 14/39 3) 10/13 4) 12/13 Solution: Option (2) 14/39 Let R be the red balls and W be the white ball In a box, B1 contains 1R, 2W... View Article

If 5 Cos 2 Theta 2 Cos 2 Theta 2 1 Theta Where 0 Theta Pi Then

If 5 cos 2θ + 2 cos2 θ/2 + 1 = 0, where 0 < θ < π, then the value of θ 1) π/3 ± π 2) π/3, cos-1(3/5) 3) cos-1(3/5) ± π 4) π/3, π -... View Article

The Solutions Of The Equation 4 Cos 2 X 6 Sin 2 X 5 Are

1) x = nπ ± π/4 2) x = nπ ± π/3 3) x = nπ ± π/2 4) x = nπ ± 2π/3 Answer: (1) x = nπ ± π/4 Solution: Given, 4 cos2x + 6 sin2x = 5 4... View Article