Question Detail

A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.

52/55
3/55
41/44
3/44

Answer: Option C

Explanation:

\begin{aligned}
\text{Total cases =} ^{12}C_3 \\
= \frac{12*11*10}{3*2*1} = 220 \\
\text{Total cases of drawing same colour =} \\
^{5}C_3 + ^{4}C_3 + ^{3}C_3 \\
\frac{5*4}{2*1} + 4 + 1 = 15 \\

\text{Probability of same colur =} = \frac{15}{220}\\
= \frac{3}{44} \\

\text{Probability of not same colur =} \\
1-\frac{3}{44}\\ = \frac{41}{44}

\end{aligned}

1. From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are kings

2/121
2/221
1/221
1/13

Answer: Option C

Explanation:

\begin{aligned}
\text{Total cases =} ^{52}C_2 \\
= \frac{52*51}{2*1} = 1326 \\
\text{Total King cases =} ^{4}C_2 \\
= \frac{4*3}{2*1} = 6 \\

\text{Probability =} = \frac{6}{1326}\\
= \frac{1}{221} \\
\end{aligned}

2. Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white

Answer: Option B

Explanation:

Total cases = 10 + 20 = 30
Favourable cases = 20

So probability = 20/30 = 2/3

3. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?

2/3
8/21
3/7
9/22

Answer: Option B

Explanation:

Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.

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

1/13
2/13
1/26
1/52

Answer: Option C

Explanation:

Total number of cases = 52
Favourable cases = 2

Probability = 2/56 = 1/26

5. From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.

3/13
1/52
1/4
None of above

Answer: Option A

Explanation:

Total number of cases = 52

Total face cards = 12 [favourable cases]

So probability = 12 /52 = 3/13