Problem

A bag contains 7 red marbles, 2 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest $10 t h$ of a percent, that both marbles drawn will be blue?

Solution

Step 1 :Calculate the total number of marbles: 7 red + 2 blue + 5 green = 14 marbles

Step 2 :Find the total number of possible outcomes when drawing two marbles: \(\binom{14}{2} = 91\)

Step 3 :Find the number of successful outcomes (drawing 2 blue marbles): \(\binom{2}{2} = 1\)

Step 4 :Calculate the probability: \(\frac{1}{91} \approx 0.011\)

Step 5 :Convert the probability to a percentage: \(0.011 \times 100 = 1.1\%\)

Step 6 :\(\boxed{1.1\%}\)

From Solvely APP
Source: https://solvelyapp.com/problems/13149/

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