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What is the probability showing the formula of choosing 4 red marbles out of a bag with 5 red marbles and 10 blue marbles?
Wiki User
∙ 8y ago
Probability = number_of_ways_of_success/total_number_of_ways
If two events are independent, their probabilities are multiplied together, eg tossing a coin to get heads and throwing a 6 with a single [standard cube] die.
In this case, I guess you are choosing 4 marbles at random. This is the same as choosing one marble, then choosing the next WITHOUT replacing the first marble; each random choice of marble is independent of the previous in so far as the colour only depends upon what is left in the bag.
So the probability here is the product of the probability that the first marble is red, the next marble (without the first being replaced) is red and so on until 4 have been chosen:
Pr(1st red) = 5/15 (= 1/3) as there are 5 red marbles and 5+10=15 marbles in the bag
Pr(2nd red) = 4/14 (= 2/7) as there are now only 4 red and 4+10 = 14 marbles in the bag
Pr(3rd red) = 3/13 as there are now only 3 red marbles and 3+10 = 13 marbles in the bag
Pr(4th red) = 2/12 (= 1/6) as there are now 2 red marbles and 2+10 = 12 marbles in the bag.
Thus Pr(4 red) = Pr(1st red) × Pr(2nd red) × Pr(3rd red) × Pr(4th red)
→ Pr(4 red) = 1/3 × 2/7 × 3/13 × 1/6 = 1/273 ≈ 0.00366 ≈ 0.366 %
Wiki User
∙ 8y ago
Wiki User
∙ 8y ago1 out of 273 is the probability.
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