Three coins are tossed. Describe Two events, which are not mutually exclusive.
When three coins are tossed, the sample space is given by
$S =\{ HHH , \,HHT , \,HTH ,\, HTT , \,THH , \,THT , \,TTH , \,TTT \}$
Two events that are not mutually exclusive can be
$A:$ getting three heads
$B:$ getting at least $2$ heads
ie. $A=\{H H H\}$
$B =\{ HHH , \,HHT , \,HTH ,\, THH \}$
This is because $A \cap B=\{H H H\} \neq \phi$
From a pack of $52$ cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is
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 probability of getting at least one tail in $4$ throws of a coin is
A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is