(C) The prime numbers in the set of values for $X$ are $\{2, 3, 5, 7\}$.$P(E) = P(X=2) + P(X=3) + P(X=5) + P(X=7) = 0.23 + 0.12 + 0.08 + 0.05 = 0.48$.

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(C) The prime numbers in the set of values for $X$ are $\{2, 3, 5, 7\}$.$P(E) = P(X=2) + P(X=3) + P(X=5) + P(X=7) = 0.23 + 0.12 + 0.08 + 0.05 = 0.48$.The event $F = \{X $P(F) = P(X=1) + P(X=2) + P(X=3) + P(X=4) = 0.15 + 0.23 + 0.12 + 0.20 = 0.70$.The event $E \cap F$ represents $X$ being a prime number less than $5$,which is $\{2, 3\}$.$P(E \cap F) = P(X=2) + P(X=3) = 0.23 + 0.12 = 0.35$.Using the addition theorem of probability:$P(E \cup F) = P(E) + P(F) - P(E \cap F)$$P(E \cup F) = 0.48 + 0.70 - 0.35 = 0.83$.

Class 12 Mathematics Probability Mix Examples-Probability

Easy

$A$ random variable $X$ has the following probability distribution:
| $X=x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| $P(X=x)$ | $0.15$ | $0.23$ | $0.12$ | $0.20$ | $0.08$ | $0.10$ | $0.05$ | $0.07$ |
For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 5\}$,find $P(E \cup F)$.

MHT CET 2023 All MHT CET

A
$0.63$
B
$0.75$
C
$0.83$
D
$0.90$

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Consider the system of equations $ax+by=0, cx+dy=0$,where $a, b, c, d \in \{0, 1\}$.
$STATEMENT-1$: The probability that the system of equations has a unique solution is $3/8$.
$STATEMENT-2$: The probability that the system of equations has a solution is $1$.

IIT 2008

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DifficultJEE MAIN 2018

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EasyMHT CET 2020

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EasyAP EAMCET 2019

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MediumIIT 1983

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Consider the system of equations $ax+by=0, cx+dy=0$,where $a, b, c, d \in \{0, 1\}$.$STATEMENT-1$: The probability that the system of equations has a unique solution is $3/8$.$STATEMENT-2$: The probability that the system of equations has a solution is $1$.

$A$ bag contains $4$ red and $6$ black balls. $A$ ball is drawn at random from the bag,its colour is observed,and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag,then the probability that this drawn ball is red,is:

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Consider the system of equations $ax+by=0, cx+dy=0$,where $a, b, c, d \in \{0, 1\}$.
$STATEMENT-1$: The probability that the system of equations has a unique solution is $3/8$.
$STATEMENT-2$: The probability that the system of equations has a solution is $1$.