A coin is tossed three times in succession. I | vedclass

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

Question

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. Total number of outcomes $n(S) = 8$. Eve

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) The sample space $S$ for tossing a coin three times is: $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. Total number of outcomes $n(S) = 8$. Event $E$ is the event of getting at least two heads: $E = \{HHH, HHT, HTH, THH\}$,so $n(E) = 4$. Event $F$ is the event that the first throw is a head: $F = \{HHH, HHT, HTH, HTT\}$,so $n(F) = 4$. The intersection $E \cap F$ is the set of outcomes where there are at least two heads $AND$ the first throw is a head: $E \cap F = \{HHH, HHT, HTH\}$,so $n(E \cap F) = 3$. The conditional probability is given by: $P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{n(E \cap F)}{n(F)} = \frac{3}{4}$.

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P(E|F) = $

Similar Questions

$A$ box contains $10$ mangoes,out of which $4$ are rotten. $2$ mangoes are taken out together. If one of them is found to be good,what is the probability that the other is also good?

Two integers are selected at random from the set $\{1, 2, \dots, 11\}.$ Given that the sum of the selected numbers is even,what is the conditional probability that both numbers are even?

If $E_1$ and $E_2$ are two events of a sample space such that $P(E_1) = \frac{1}{4}$,$P(E_2 \mid E_1) = \frac{1}{2}$,and $P(E_1 \mid E_2) = \frac{1}{4}$,then $P(\bar{E}_1 \mid E_2) = $

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

Let $A, B$ and $C$ be three events,which are pairwise independent and $\overline{E}$ denote the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$,then $P((\overline{A} \cap \overline{B}) / C)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module