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  • Assuming the balls to be identical except for the difference in colors, if you randomly select two balls from 10 red, 7 blue, and 6 yellow balls, what is the probability of red balls selected for t

Assuming the balls to be identical except for the difference in colors, if you randomly select two balls from 10 red, 7 blue, and 6 yellow balls, what is the probability of red balls selected for the first draw
and yellow in the second draw?

Option: 1

0.51


Option: 2

0.23


Option: 3

0.45


Option: 4

0.11


Answers (1)

best_answer

To find the probability of selecting red balls for the first draw and yellow balls for the second draw,
we need to calculate the probability of each possible outcome.

The probability of selecting a red ball on the first draw is given by the ratio of the number of red balls
to the total number of balls:
P(Red on first draw) = (number of red balls) / (total number of balls)

After the first draw, there will be 9 balls remaining, out of which 6 are yellow. The probability of
selecting a yellow ball on the second draw is given by the ratio of the number of yellow balls to the
total number of balls remaining:
P(Yellow on second draw) = (number of yellow balls) / (total number of balls remaining)

To find the overall probability of selecting red balls for the first draw and yellow balls for the second
draw, we multiply the probability of red on the first draw by the probability of yellow on the second
draw:

Overall probability = P(Red on first draw) \times P(Yellow on second draw)

Let's calculate the values:
\mathrm{P( \text{Red on first draw} )=10 /(10+7+6)=10 / 23}
\mathrm{\mathrm{P}(\text{ Yellow on second draw} )=6 /(9+7+6)=6 / 22=3 / 11}
\mathrm{Overall \: probability =(10 / 23) \times(3 / 11)=30 / 253 \approx 0.1183}
Therefore, the probability of selecting red balls for the first draw and yellow balls for the second draw is approximately 0.1183 , or 11.83 \%.
 

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Pankaj

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