A coin is tossed three times, consider the following events.
$A: $ ' No head appears ', $B:$ ' Exactly one head appears ' and $C:$ ' Atleast two heads appear '
Do they form a set of mutually exclusive and exhaustive events?
A coin is tossed three times, consider the following events.
$A: $ ' No head appears ', $B:$ ' Exactly one head appears ' and $C:$ ' Atleast two heads appear '
Do they form a set of mutually exclusive and exhaustive events?
The sample space of the experiment is
$S =\{ HHH ,\, HHT ,\, HTH$ , $THH ,\, HTT , THT$, $TTH, \,TTT\}$
and $A=\{ TTT \}$, $B =\{ HTT , \,THT, \, TTH \}$, $C =\{ HHT \,, HTH ,\, THH , \,HHH \}$
Now
$A \cup B \cup C =$ $\{ TTT , \, H T T , \, T H T $, $T T H , \, H H T $, $H T H , \, T H H , \, H H H \} \, = S$
Therefore, $A, \,B$ and $C$ are exhaustive events.
Also, $A \cap B=\phi, A \cap C=\phi$ and $B \cap C=\phi$
Therefore, the events are pair-wise disjoint, i.e., they are mutually exclusive.
Hence, $A,\, B$ and $C$ form a set of mutually exclusive and exhaustive events.
Similar Questions
The probability that a teacher will give an unannounced test during any class meeting is $1/5$. If a student is absent twice, then the probability that the student will miss at least one test is
The probability that a teacher will give an unannounced test during any class meeting is $1/5$. If a student is absent twice, then the probability that the student will miss at least one test is
One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a diamond
One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a diamond
The probability that an ordinary or a non-leap year has $53$ sunday, is
The probability that an ordinary or a non-leap year has $53$ sunday, is
Three coins are tossed. Describe Three events which are mutually exclusive and exhaustive.
Three coins are tossed. Describe Three events which are mutually exclusive and exhaustive.
Two persons each make a single throw with a die. The probability they get equal value is ${p_1}$. Four persons each make a single throw and probability of three being equal is ${p_2}$, then
Two persons each make a single throw with a die. The probability they get equal value is ${p_1}$. Four persons each make a single throw and probability of three being equal is ${p_2}$, then