A coin is tossed until a head appears or it h | vedclass

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

Question

(A) Let $H$ denote the event of getting a head and $T$ denote the event of getting a tail. The experiment stops when a head appears or after three tos

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) Let $H$ denote the event of getting a head and $T$ denote the event of getting a tail. The experiment stops when a head appears or after three tosses.The sample space of the experiment is $S = \{H, TH, TTH, TTT\}$.Let $A$ be the event that a head does not appear on the first toss. This means the first toss is a tail $(T)$.The outcomes corresponding to event $A$ are $\{TH, TTH, TTT\}$.The probability $P(A) = P(T) = \frac{1}{2}$.Let $B$ be the event that the coin is tossed thrice. The outcomes corresponding to event $B$ are $\{TTH, TTT\}$.The intersection $A \cap B$ represents the event that the first toss is a tail $AND$ the coin is tossed thrice. This corresponds to the outcomes $\{TTH, TTT\}$.$P(A \cap B) = P(TTH) + P(TTT) = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$.We need to find the conditional probability $P(B|A)$:$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}$.

$A$ coin is tossed until a head appears or it has been tossed thrice. Given that a head does not appear on the first toss,what is the probability that the coin is tossed thrice?

Similar Questions

Let $A, B, C$ be pairwise independent events such that $P(C) > 0$ and $P(A \cap B \cap C) = 0$. Then $P(A' \cap B'|C)$ is equal to:

If the events $A$ and $B$ are mutually exclusive,then $P\left( \frac{A}{B} \right) = $

Bag $P$ contains $3$ white,$2$ red,$5$ blue balls and bag $Q$ contains $2$ white,$3$ red,$5$ blue balls. $A$ ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random,then the probability that it is a red ball is

If $A$ and $B$ are two events such that $P(A) = \frac{3}{8}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A|B) = $

When a die is thrown twice,what is the probability that the sum of the numbers is $6$,given that at least one of the numbers is $4$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module