Three coins are tossed. Describe two events which are mutually exclusive.
(N/A) When three coins are tossed,the sample space $S$ is given by:
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events $A$ and $B$ are mutually exclusive if they have no common outcomes,i.e.,$A \cap B = \emptyset$.
Let $A$ be the event of getting no heads: $A = \{TTT\}$.
Let $B$ be the event of getting no tails: $B = \{HHH\}$.
Since $A \cap B = \emptyset$,these two events are mutually exclusive.
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Two events $A$ and $B$ are mutually exclusive if they have no common outcomes,i.e.,$A \cap B = \emptyset$.
Let $A$ be the event of getting no heads: $A = \{TTT\}$.
Let $B$ be the event of getting no tails: $B = \{HHH\}$.
Since $A \cap B = \emptyset$,these two events are mutually exclusive.
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Similar Questions
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?
$A:$ 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?
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View SolutionThe probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$,then $P(A') + P(B') = $
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View SolutionTwo dice are thrown simultaneously. The probability of obtaining a total score of $5$ is
Let $A$ and $B$ be events in a sample space $S$ such that $P(A)=0.5, P(B)=0.4$ and $P(A \cup B)=0.6$. Observe the following lists. The correct match of List $I$ from List $II$ is:
List $I$ List $II$ $(i) \ P(A \cap B)$ $(1) \ 0.4$ $(ii) \ P(A \cap \bar{B})$ $(2) \ 0.2$ $(iii) \ P(\bar{A} \cap B)$ $(3) \ 0.3$ $(iv) \ P(\bar{A} \cap \bar{B})$ $(4) \ 0.1$
| List $I$ | List $II$ |
| $(i) \ P(A \cap B)$ | $(1) \ 0.4$ |
| $(ii) \ P(A \cap \bar{B})$ | $(2) \ 0.2$ |
| $(iii) \ P(\bar{A} \cap B)$ | $(3) \ 0.3$ |
| $(iv) \ P(\bar{A} \cap \bar{B})$ | $(4) \ 0.1$ |
$A$ bag contains $3$ white and $7$ red balls. If a ball is drawn at random,what is the probability that the drawn ball is either white or red?
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