JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Probability

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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

Solution

Drawing 3 from 5 blue + 4 yellow.

E [X]

for blue (hypergeometric)

= 3 \cdot \frac{5}{9} = \frac{5}{3}

, and

\overset{ˉ}{X} = \frac{5}{3}

gives

7 \overset{ˉ}{X} = \frac{35}{3}

. For yellow

E [Y] = 3 \cdot \frac{4}{9} = \frac{4}{3}

, so

4 \overset{ˉ}{Y} = \frac{16}{3}

. Then

7 \overset{ˉ}{X} + 4 \overset{ˉ}{Y} = \frac{35 + 16}{3} = \frac{51}{3} = 17

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Integer answer

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