Two cards are drawn from a pack of 52 playing | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Case $1$: With replacement.$p_1 = P(	ext{First is Queen}) 	imes P(	ext{Second is Diamond}) = \frac{4}{52} 	imes \frac{13}{52} = \frac{1}{13} \

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Case $1$: With replacement.$p_1 = P(	ext{First is Queen}) 	imes P(	ext{Second is Diamond}) = \frac{4}{52} 	imes \frac{13}{52} = \frac{1}{13} 	imes \frac{1}{4} = \frac{1}{52}$.Case $2$: Without replacement.Let $Q_1$ be the event that the first card is a queen and $D_2$ be the event that the second card is a diamond.If the first card is the Queen of Diamonds, $P(Q_1 \cap D_2) = P(Q_1 \cap D_1) 	imes P(D_2 | Q_1 \cap D_1) = \frac{1}{52} 	imes \frac{12}{51}$.If the first card is a Queen other than the Queen of Diamonds, $P(Q_1 \cap D_2) = P(Q_1 \cap D_1^c) 	imes P(D_2 | Q_1 \cap D_1^c) = \frac{3}{52} 	imes \frac{13}{51}$.$p_2 = \frac{1 	imes 12 + 3 	imes 13}{52 	imes 51} = \frac{12 + 39}{52 	imes 51} = \frac{51}{52 	imes 51} = \frac{1}{52}$.Therefore, $\frac{p_1}{p_2} = \frac{1/52}{1/52} = 1$.

Similar Questions

$A$ fair die is tossed until a six is obtained. Let $X$ be the number of required tosses,then the conditional probability $P(X \geq 5 \mid X > 2)$ is:

If $A$ and $B$ are two independent events,then $A$ and $\bar{B}$ are

$A$ cubical die with faces marked $1, 2, 3, ..., 6$ is tossed such that the probability of throwing the number $t$ is proportional to $t^2$. The probability that the number $5$ has appeared,given that the number turned up is not even,is:

Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$, $P(B) = 0.4$, and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

If $A$ and $B$ are two events such that $P(A \cap B) = 0.1$,and $P(A \mid B)$ and $P(B \mid A)$ are the roots of the equation $12x^2 - 7x + 1 = 0$,then the value of $\frac{P(\overline{A} \cup \overline{B})}{P(\overline{A} \cap \overline{B})}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module