Navigate

Question Detail

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}

Similar Questions :

1. Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

  • 1/3
  • 1/6
  • 1/2
  • 1/8

Answer: Option C

Explanation:

Total cases are = 2*2*2 = 8, which are as follows
[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]

Favoured cases are = [TTH, THT, HTT, TTT] = 4

So required probability = 4/8 = 1/2

2. 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

3. In a throw of dice what is the probability of getting number greater than 5

  • 1/2
  • 1/3
  • 1/5
  • 1/6

Answer: Option D

Explanation:

Number greater than 5 is 6, so only 1 number
Total cases of dice = [1,2,3,4,5,6]

So probability = 1/6

4. There is a pack of 52 cards and Rohan draws two cards together, what is the probability that one is spade and one is heart ?

  • 11/102
  • 13/102
  • 11/104
  • 11/102

Answer: Option B

Explanation:

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

Let sample space be S
\begin{aligned}
\text{then, n(S) = }^{52} C _2 \\
=> \frac{52 \times 51}{ 2 \times 1} = 1326 \\
\text {let E be event of getting 1 spade and 1 heart} \\
\text{So, n(E) = ways of getting 1 spade or 1 heart out of 13} \\
= ^{13}C_1 \times ^{13}C_1 \\
= 13 \times 13 \\
= 169 \\
\text{So, p(E) = }\frac{n(E)}{n(S)} \\
= \frac{169}{1326} = \frac{13}{102}
\end{aligned}

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

  • 1
  • 2/3
  • 1/3
  • 4/3

Answer: Option B

Explanation:

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

So probability = 20/30 = 2/3

Read more from - Probability Questions Answers