In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

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: 2/7

Explanation:

1 year = 365 days . A leap year has 366 days

A year has 52 weeks. Hence there will be 52 Sundays for sure.

52 weeks = 52 x 7 = 364days

366 ? 364 = 2 days

In a leap year there will be 52 Sundays and 2 days will be left.

These 2 days can be:

1. Sunday, Monday

2. Monday, Tuesday

3. Tuesday, Wednesday

4. Wednesday, Thursday

5. Thursday, Friday

6. Friday, Saturday

7. Saturday, Sunday

Of these total 7 outcomes, the favourable outcomes are 2.

Hence the probability of getting 53 days = 2/7

Correct Answer: 5/12

Explanation:

Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

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

n(E) = 15.

P(E) = n(E)/n(S) = 15/36 = 5/12.

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: 13/102

Explanation:

Let S be the sample space.

 

Then, n(S) = 52 C 2=(52 x 51)/(2 x 1) = 1326.

 

Let E = event of getting 1 spade and 1 heart.

 

n(E)= number of ways of choosing 1 spade out of 13 and 1 heart out of 13 =  13 C 1 * 13 C 1 = 169.

 

P(E) = n(E)/n(S) = 169/1326 = 13/102.

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.