Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityRandom Variable and its Probability DistributionMedium2 minPYQ_2024

MathematicsMediumnumerical

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\overset{ˉ}{X}$ and $\overset{ˉ}{Y}$ are the means of $X$ and $Y$ respectively, then $7 \overset{ˉ}{X} + 4 \overset{ˉ}{Y}$ is equal to________

Answer:

17.00

Solution:

$7 \overline{x} = \frac{^{5} C _{1} ^{4} C _{2} + ^{5} C _{2} \cdot ^{4} C _{1} \times 2 + ^{5} C _{3} \cdot ^{4} C _{0} \times 3}{^{9} C _{3}} \times 7 \frac{30 + 80 + 30}{84} \times 7 = \frac{140}{12} = \frac{70}{6} = \frac{35}{3}$
$ye ll o w 0 1^{5} C_{2}^{4} C_{1} 2^{5} C_{1}^{4} C_{2} 3^{5} C_{0}^{4} C_{3} 40$
$4 \overset{y}{ˉ} = \frac{40 + 60 + 12}{84} \times 4 = \frac{112}{21} = \frac{16}{3}$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:Random Variable and its Probability Distribution

⏱ 2mℹ️ Source: PYQ_2024

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