Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

Correct Answer: 316/435

Explanation:

n s = C 2 30

 

 Let A be the event of getting two oranges and 

 

 B be the event of getting two non-defective fruits.

 

 and  A ? B be the event of getting two non-defective oranges

 

  ? P A = C 2 20 C 2 30 , P B = C 2 22 C 2 30 a n d P A ? B = C 2 15 C 2 30

 

  ? P A ? B = P A + P B - P A ? B

 

=  C 2 20 C 2 30 + C 2 22 C 2 30 - C 2 15 C 2 30 = 316 435

Correct Answer: 21/46

Correct Answer: 19/90

Explanation:

A S S I S T A N T ? A A I N S S S T T

S T A T I S T I C S ? A C I I S S S T T T

Here N and C are not common and same letters can be A, I, S, T. Therefore

 Probability of choosing A =   2 C 1 9 C 1 × 1 C 1 10 C 1 = 1/45 

 Probability of choosing I =  1 9 C 1 × 2 C 1 10 C 1 = 1/45

Probability of choosing S =  3 C 1 9 C 1 × 3 C 1 10 C 1 = 1/10

Probability of choosing T =  2 C 1 9 C 1 × 3 C 1 10 C 1 = 1/15

Hence, Required probability =    1 45 + 1 45 + 1 10 + 1 15 = 19 90 

Correct Answer: 7/18

Explanation:

Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.
Then,E = {(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)}
n(E) = 14.
Hence, P(E) = n(E)/n(S) = 14/36 = 7/18

Correct Answer: 2/91

Explanation:

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15 =  15 C 3  = 15 * 14 * 13 3 * 2 * 1= 455.  

Let E = event of getting all the 3 red balls.

 n(E) = 5 C 3 = 5 * 4 2 * 1 = 10.

 => P(E) = n(E)/n(S) = 10/455 = 2/91.

Correct Answer: 4/7

Explanation:

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) = 8 /14 = 4/7.

Correct Answer: 1/2

Explanation:

Here S= {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}.

Let E = event of getting at least two heads = {THH, HTH, HHT, HHH}.

P(E) = n(E) / n(S)

      = 4/8= 1/2

Correct Answer: 3/13

Explanation:

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = 12/52=3/13.

Correct Answer: 15/39

Explanation:

P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize) 

 

 =  1 - 16 C 1 × 14 C 1 × 12 C 1 × 10 C 1 16 C 4 = 15 39

Correct Answer: 1/6

Explanation:

P(first letter is not vowel) =  2 4

 

P(second letter is not vowel) =  1 3

 

So, probability that none of letters would be vowels is =  2 4 × 1 3 = 1 6