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Q:

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A) 2/91	B) 1/22
C) 3/22	D) 2/77

Answer & Explanation Answer: A) 2/91

Explanation:

Let S be the sample space.

Then, n(S) = number of ways of drawing 3 balls out of 15 = $15 C_{3}$ = $\frac{15 * 14 * 13}{3 * 2 * 1}$ = 455.

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

n(E) = $5 C_{3}$ = $\frac{5 * 4}{2 * 1}$ = 10.

=> P(E) = n(E)/n(S) = 10/455 = 2/91.

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Q:

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

A) 3/20	B) 29/34
C) 47/100	D) 13/102

Answer & Explanation Answer: D) 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.

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Q:

In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:

A) 21 m	B) 26 m
C) 28m	D) 29m

Answer & Explanation Answer: C) 28m

Explanation:

A : B = 100 : 75

B : C = 100 : 96.

A : C = (A/B*B/C) = (100/75*100/96) = 100/72 =100:72

A beats C by (100 - 72) m = 28 m.

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Filed Under: Races and Games

Q:

A runs $1 \frac{2}{3}$ times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

A) 200 m	B) 300m
C) 270m	D) 160m

Answer & Explanation Answer: A) 200 m

Explanation:

Ratio of the speeds of A and B =5 : 1 = 5 :3

Thus, in race of 5 m, A gains 2 m over B.

2 m are gained by A in a race of 5 m.

80 m will be gained by A in race of $(\frac{5}{2} * 80)$ m =200m

=> Winning post is 200 m away from the starting point.

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Filed Under: Races and Games

Q:

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a

king of heart is:

A) 2/13	B) 1/13
C) 1/26	D) 1/52

Answer & Explanation Answer: C) 1/26

Explanation:

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) =n(E)/n(S)=2/52=1/26.

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Q:

A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:

A) 100 m	B) 75 m
C) 25 m	D) 50m

Answer & Explanation Answer: A) 100 m

Explanation:

When B runs 25 m, A runs 45/2 m

When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.

B beats A by 100 m.

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Filed Under: Races and Games

Q:

In a 200 metres race A beats B by 35 m or 7 seconds. A's time over the course is:

A) 40 sec	B) 47sec
C) 33sec	D) none of these

Answer & Explanation Answer: C) 33sec

Explanation:

B runs 35 m in 7 sec.

B covers 200 m in (7/35*200) = 40 sec.

B's time over the course = 40 sec.

A's time over the course (40 - 7) sec = 33 sec.

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Filed Under: Races and Games

Q:

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

A) 8 points	B) 10 points
C) 14points	D) 40points

Answer & Explanation Answer: B) 10 points

Explanation:

A : B = 100 : 80.

A : C = 100 : 72.

B:C = B/A*A/C = 80/10*100/72 = 10/9 = 100/90 = 100:90

B can give C 10 points

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Filed Under: Races and Games

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