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13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
A random variable $X$ has the probability distribution  ....For the events $E = \{ X$is prime number $\}$ and $F = \{ X < 4\} $, the probability of $P(E \cup F)$ is
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P(X)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
  • A
    $0.5$
  • ✓
    $0.77$
  • C
    $0.35$
  • D
    $0.87$
✓

Answer

Correct option: B.
$0.77$
b
(b) $E = \{ x$ is a prime number $\}$

$P(E) = P(2) + P(3) + P(5) + P(7) = 0.62,\,$

$F = \{ x < 4\} $, $P(F) = P(1) + P(2) + P(3) = 0.50$

and $P(E \cap F) = P(2) + P(3) = 0.35$

$\therefore $ $P(E \cup F) = P(E) + P(F) - P(E \cap F)$

$= 0.62+0.50 -0.35 = 0.77.$

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