There are 100 marbles in a jar. Forty of the marbles are black and 60

Probability of getting AT LEAST 1 Black marble = 1-(Probability of getting white marble)

Hence,
=1-(60/100)(60/100)(60/100)
=1-(0.6)^3
=1-0.216
=0.784

Note:Use cube of 6 to get the answer quickly.

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Solution:

We can use the equation:

P(at least one black marble) = 1 - P(no black marbles)

P(at least one black marble) = 1 - P(all white marbles)

P(at least one black marble) = 1 - (3/5 x 3/5 x 3/5)

P(at least one black marble) = 1 - 27/125 = 1 - 216/1000 = 1 - 0.216 = 0.784

Alternate Solution:

The long way is to consider that any of the following cases will satisfy the requirement:

Case 1. One black and two white: BWW, WBW, WWB, and each outcome has a probability of 2/5 x 3/5 x 3/5 = 18/125. Because there are 3 different outcomes, multiply by 3 to get 54/125.

Case 2. Two black and one white: WBB, BWB, BBW , and each outcome has a probability of 3/5 x 2/5 x 2/5 = 12/125. Because there are 3 different outcomes, multiply by 3 to get 36/125

Case 3. Three black: BBB, with probability 2/5 x 2/5 x 2/5 = 8/125.

Thus, the probability of getting at least one black marble is the sum: 54/125 + 36/125 + 8/125 = 98/125.= 0.784.

Answer: E