1. Tardigrade
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  4. A random variable X has the probability distribution: X 1 2 3 4 5 6 7 8 P(X) 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 For the events E = X is a prime number and F = X <4 the probability P ( E ∪ F ) is

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Q. A random variable $X$ has the probability distribution:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$

For the events $E =\{ X$ is a prime number $\}$ and $F =\{ X <4\}$, the probability $P ( E \cup F )$ is

VITEEEVITEEE 2017

Solution:

$P ( E )= P$ ($2$ or $3$ or $5$ or $7$)
$=0.23+0.12+0.20+0.07=0.62$
$P ( F )= P$ ($1$ or $2$ or $3$)
$=0.15+0.23+0.12=0.50$
$P(E \cap F)=P$ ($2$ or $3$)
$=0.23+0.12=0.35$
$\therefore P(E U F)=P(E)+P(F)-P(E \cap F)$
$=0.62+0.50-0.35=0.77$