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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
A random variable $X$ has the following probability distribution:
$X:$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$
$P(X):$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
Find the events $E = \{X : X$ is a prime number$\}, F\{X :X < 4\},$ the probability $\text{P}(\text{E}\cup\text{F})$ is:
  • ✓
    $0.50$
  • B
    $0.77$
  • C
    $0.35$
  • D
    $0.87$
✓

Answer

Correct option: A.
$0.50$
$P(E) = P(2) + P(3) + P(5) + P(7)$
$P(E) = 0.23 + 0.12 + 0.20 + 0.07$
$P(E) = 0.62$
And
$P(F) = P(1) + P(2) + P(3)$
$P(F) = 0.15 + 0.23 + 0.12$
$P(F) = 0.5$
Also,
$\text{P}(\text{E}\cap\text{F})=\text{P}(2)+\text{P}(3)$
$\text{P}(\text{E}\cap\text{F})=0.23+0.12$
$\text{P}(\text{E}\cap\text{F})=0.35$
$\text{P}(\text{E}\cup\text{F})=\text{P}(\text{E})+\text{P(F)}-\text{P}(\text{E}\cap\text{F})$
$\text{P}(\text{E}\cup\text{F})=0.62+0.5-0.35$
$\text{P}(\text{E}\cup\text{F})=0.77$

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