Events and its Types

Find the probability that a number selected at random from the numbers $3, 4, 4, 4, 5, 5, 6, 6, 6, 7$will be their mean.

A word consists of 10 different alphabets, in which there are 4 consonants and 6 vowels. Four alphabets are chosen at random. What is the probability that more than one vowel is selected?

 A town has two doctors x and y operating independently.if the probability that the doctor x is available is 0.9 and that for y is 0.8,then find out the probability that at least one doctor is available when needed.

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?

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment

$A$: 'the sum is even'.

$B$: 'the sum is a multiple of $3$'.

$C$: 'the sum is less than $4$'.

$D$: 'the sum is greater than $11$'.

Which pairs of these events are mutually exclusive?

For any two events $\mathrm{A}$ and $\mathrm{B}$:

In the experiment of rolling a single die, find the intersection of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than one.”

In the experiment of rolling a single die, find the intersection of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than two.”

In the experiment of rolling a single die, find the intersection of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than three.”

In the experiment of rolling a single die, find the intersection of the events $E$: “the number rolled is even” and $T$: “the number rolled is greater than three.”

In the experiment of rolling a single die, find the intersection of the events $E$: “the number rolled is even” and $T$: “the number rolled is greater than four.”

In the experiment of rolling a single die, find the union of the events $E$: “the number rolled is even” and $T$: “the number rolled is greater than four.”

In the experiment of rolling a single die, find the union of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than four.”

In the experiment of rolling a single die, find the union of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than three.”

In the experiment of rolling a single die, find the union of the events $E$: “the number rolled is odd” and $T$: “the number rolled is greater than two.”

In the experiment of rolling a single die, find the union of the events $E$: “the number rolled is even” and $T$: “the number rolled is greater than two.”

Find the total number of elementary events associated with the random experiment of rolling a pair of dice together.

Find the total number of elementary events associated with the random experiment of tossing two coins.

Find the total number of elementary events when a coin is tossed.