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Q:

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A) 1/15	B) 1/221
C) 25/57	D) 35/256

Answer & Explanation Answer: B) 1/221

Explanation:

Let S be the sample space

Then, n(S) = $52 C_{2}$ = 1326.

Let E = event of getting 2 kings out of 4.

n(E) = $\frac{52 * 51}{2 * 1}$ = 6.

$4 C_{2}$

=> $\frac{4 * 3}{2 * 1}$

$P (E) = \frac{n (E)}{n (S)} = \frac{6}{1326} = \frac{1}{221}$

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Q:

At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?

A) 30 points	B) 20 points
C) 10 points	D) 12 points

Answer & Explanation Answer: C) 10 points

Explanation:

A : B = 60 : 45.

A : C = 60 : 40.

B/C = (B/A*A/C) = (45/60*60/45) = 45/40 = 90/80 = 90:80

B can give C 10 points in a game of 90.

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Filed Under: Races and Games

Q:

In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:

A) 5.4m	B) 4.5m
C) 5m	D) 6m

Answer & Explanation Answer: D) 6m

Explanation:

A : B = 100 : 90.

A : C = 100 : 87.

B/C = (B/A*A/C) = (90/100*100/87) = 30/29

When B runs 30 m, C runs 29 m.

When B runs 180 m, C runs (29/30*180)m =174m

B beats C by (180 - 174) m = 6 m.

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Q:

In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:

A) 60m	B) 40m
C) 20m	D) 10m

Answer & Explanation Answer: C) 20m

Explanation:

To reach the winning post A will have to cover a distance of (500 - 140)m, i.e., 360 m.

While A covers 3 m, B covers 4 m.

While A covers 360 m, B covers (4/3)*360 = 480 m.

Thus, when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.

A wins by 20 m.

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Filed Under: Races and Games

Q:

A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:

A) 5.15 kmph	B) 4.14 kmph
C) 4.25 kmph	D) 4.4 kmph

Answer & Explanation Answer: B) 4.14 kmph

Explanation:

A's speed = (5*5/15)m/sec = (25/18)m/sec

Time taken by A to cover 100 m = (100*18/15)sec = 72sec

Time taken by B to cover 92 m = (72 + 8) = 80 sec.

B's speed =(92/80*18/5)kmph =4.14kmph

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Q:

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A) 2/7	B) 5/7
C) 1/5	D) 1/2

Answer & Explanation Answer: A) 2/7

Explanation:

Total number of outcomes possible, n(S) = 10 + 25 = 35

Total number of prizes, n(E) = 10

$P (E) = \frac{n (E)}{n (S)} = \frac{10}{35} = \frac{2}{7}$

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Q:

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:

A) 21/46	B) 1/5
C) 3/25	D) 1/50

Answer & Explanation Answer: A) 21/46

Explanation:

Let , S - sample space E - event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25

= $25 C_{3}$

= 2300.

n(E) = $10 C_{1} \times 15 C_{2}$ = 1050.

$\therefore$ P(E) = n(E)/n(s) = 1050/2300 = 21/46

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Q:

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:

A) 21/46	B) 1/5
C) 3/25	D) 1/50

Answer & Explanation Answer: A) 21/46

Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25

= $25 C_{3}$ = 2300.

n(E)= $10 C_{1} * 15 C_{2}$ = 1050.

P(E) = n(E)/n(s) = 1050/2300 = 21/46

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