The probabilities that a student will receive an A, B, C or D grade are 0.4, 0.3 , 0.2 and 0.1 respectively. Find the probability that a student will receive Atleast B grade.

Correct Answer: 1/9

Explanation:

One person can select one house out of 3= 3 C 1 ways =3.

 

Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.

 

Therefore, probability that all thre apply for the same house is 1/9

Correct Answer: 17/42

Explanation:

3 letters can be choosen out of 9 letters in 9 C 3 ways.

 

More than one vowels ( 2 vowels + 1 consonant  or  3 vowels ) can be choosen in  ( 4 C 2 * 5 C 1 ) + 4 C 3 ways

 

Hence,required probability = 4 C 2 * 5 C 1 + 4 C 3 9 C 3 = 17/42

Correct Answer: 5/26

Explanation:

We know that,

Total number of balls n(S) = 26

Number of vowels n(E) = 5

Hence, required probability = n(E)/n(S) = 5/26.

Correct Answer: 19/42

Explanation:

A red ball can be drawn in two mutually exclusive ways

 (i) Selecting bag I and then drawing a red ball from it.

 

(ii) Selecting bag II and then drawing a red ball from it.

 

Let E1, E2 and A denote the events defined as follows:

E1 = selecting bag I,

E2 = selecting bag II

A = drawing a red ball

Since one of the two bags is selected randomly, therefore 

P(E1) = 1/2  and  P(E2) = 1/2

Now,  P A E 1 = Probability of drawing a red ball when the first bag has been selected = 4/7

   P A E 2  = Probability of drawing a red ball when the second bag has been selected = 2/6

 Using the law of total probability, we have 

 P(red ball) = P(A) =  P E 1 × P A E 1 + P E 2 × P A E 2 

 

                          =  1 2 × 4 7 + 1 2 × 2 6 = 19 42

Correct Answer: 35/100

Explanation:

Let   A = Event that A speaks the truth

B = Event that B speaks the truth 

Then P(A) = 75/100 = 3/4

P(B) = 80/100 = 4/5

P(A-lie) =  1 - 3 4= 1/4 

P(B-lie) = 1 - 4 5= 1/5

 

Now, A and B contradict each other =[A lies and B true] or [B true and B lies]

 = P(A).P(B-lie) + P(A-lie).P(B) 

 =  3 5 * 1 5 + 1 4 * 4 5 = 7 20  

 =  7 20 * 100= 35%

Correct Answer: 5/12

Explanation:

Total number of elementary events =  10 C 5

 

Number of ways of selecting exactly one defective bulb out of 3 and 4 non-defective out of 7 is  3 C 1 * 7 C 4

 

So,required probability = 3 C 1 * 7 C 4/ 10 C 5 = 5/12.

Correct Answer: 3/4

Explanation:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3,4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

n(E) = 27.

P(E) = n(E)/n(S) = 27/36 = 3/4.

Correct Answer: 1/9

Explanation:

In two throws of a die, n(S) = (6 x 6) = 36.

Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.

P(E) =n(E)/n(S)=4/36=1/9.

Correct Answer: 5/18

Explanation:

n(S) = 36

 

A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

 

B = { (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) }

 

n A = 6 , n B = 5 , n A ? B = 1

 

?Required probability =  P A ? B

 

 =  P A + P B - P A ? B

 

=   6 36 + 5 36 - 1 36 =  5 18

Correct Answer: 1/3

Explanation:

Total number of balls = (8 + 7 + 6) = 21.

Let E = event that the ball drawn is neither red nor green 

            = event that the ball drawn is blue.

n(E) = 7.

P(E) = n(E)/n(S) = 7/21 = 1/3.