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

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

Answer: Option C

Explanation:

Total cases = [H,T] - 2
Favourable cases = [T] -1
So probability of getting tails = 1/2

Answer: Option B

Explanation:

Let A = Event that A speaks the truth
B = Event that B speaks the truth

Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5

P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5

Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%

Answer: Option C

Explanation:

$$\begin{aligned} \text{Total cases =} ^{52}C_2 \\ = \frac{52*51}{2*1} = 1326 \\ \text{Total King cases =} ^{4}C_2 \\ = \frac{4*3}{2*1} = 6 \\ \text{Probability =} = \frac{6}{1326}\\ = \frac{1}{221} \\ \end{aligned}$$

Answer: Option A

Explanation:

Total number of cases = 52

Total face cards = 12 [favourable cases]



So probability = 12 /52 = 3/13