$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$?
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| $P(X)$ | $0.15$ | $0.23$ | $0.12$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
- A$0.35$
- B$0.77$
- C$0.87$
- D$0.50$
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| $X=x_i$ | $2$ | $3$ | $5$ | $7$ | $12$ |
|---|---|---|---|---|---|
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| $X = x_i$ | $0$ | $1$ | $2$ | $3$ |
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State whether the following table represents a probability distribution of a random variable $X$. Give reasons for your answer.
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