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Total balls and desired outcome
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The bag has 11 balls in all (6 black + 5 red).
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We want the probability of drawing 3 balls all black in one random draw of 3 balls.
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Count the total number of ways to choose any 3 balls
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You can pick any 3 out of 11 in “11 choose 3” ways.
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“11 choose 3” means the number of combinations of 11 items taken 3 at a time, which equals
(11 × 10 × 9) ÷ (3 × 2 × 1) = 165 total possible sets of 3 balls.
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Count the number of ways to get 3 black balls
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There are 6 black balls, and we need to pick 3 of them.
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That is “6 choose 3” = (6 × 5 × 4) ÷ (3 × 2 × 1) = 20 favourable sets.
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Form the probability
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Probability = (number of favourable sets) ÷ (total number of sets)
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So it’s 20 ÷ 165, which simplifies by dividing numerator and denominator by 5:
20 ÷ 165 = 4 ÷ 33
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Final answer
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The probability of drawing three black balls at random is 4/33 (option b).
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MCQ: Probability - 2 - SSC CGL MCQ
15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Probability - 2
In a bag, there are 13 cards of the first 13 whole numbers. If two cards are selected, what is the probability that both the cards are of prime numbers?
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Two cards are selected randomly from a deck of cards. What is the probability that both the cards are Heart cards?
If all the digits of a five-digit number are odd and different, how many such numbers are possible?
In how many ways can the letters of the word ADAMANT be arranged?
A bag contains six black and five red balls. If three balls from the bag are chosen at random, what is the probability that they are all black?
A letter is randomly choosen from the word SIGMA. Find the probability that the letter is a vowel.
There are 6 pink and 4 white balls in a bag. If two balls are drawn from the bag, what is the probability that both the balls are white?
For the arrangements of the letters of the word INDIA, how many words will start with I and end with I?
In how many ways can the letters of the word REMOTE be arranged?
If repetition is not allowed, how many numbers between 200 and 300 can be formed using digits 0, 1, 2, 3 and 5?
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MCQ: Probability - 2
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