Quantitative Reasoning

Probability

Medium

A basket contains 4 red, 5 blue and 3 green marbles. If three marbles are picked up at random, what is the probability that at least one is blue?

$\frac{37}{44}$

$\frac{7}{44}$

$\frac{7}{12}$

$\frac{5}{12}$

✅ Correct Option: 1

The basket contains:

Red marbles: 4
Blue marbles: 5
Green marbles: 3

Total marbles = 4 + 5 + 3 = 12

For "at least one blue" problems, use the complement:

P(at least one blue) = 1 - P(no blue marbles)

Total ways to pick 3 marbles from 12:

$C(12,3) = \dfrac{12 \times 11 \times 10}{3 \times 2 \times 1}$

$= \dfrac{1320}{6}$

$= 220$

Ways to pick 3 marbles with no blue (only red and green):

Non-blue marbles = 4 + 3 = 7

$C(7,3) = \dfrac{7 \times 6 \times 5}{3 \times 2 \times 1}$

$= \dfrac{210}{6}$

$= 35$

P(no blue marbles) = $\dfrac{35}{220} = \dfrac{7}{44}$

P(at least one blue) = $1 - \dfrac{7}{44}$

$= \dfrac{44}{44} - \dfrac{7}{44}$

$= \dfrac{37}{44}$

Therefore, the probability that at least one marble is blue is $\dfrac{37}{44}$ .

2025: 23 May Shift 1

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2023: 21 May Shift 1

A bag contains 5 black, 3 white and 2 red balls. Three balls are drawn in succession. What is the probability that the first ball is red, the second ball is black and the third ball is white?

2025: 24 May Shift 2

The probability that a card drawn from a pack of 52 cards will be a red card or an ace (including the chance of any red ace), is:

2025: 19 May Shift 1

A bag contains 4 red, 5 blue and 3 green balls. If two balls are drawn at random from the bag, then which of the following statements are correct?

(A) The probability that both balls are red is $\frac{1}{11}$ .

(B) The probability that one ball is red, and one ball is blue is $\frac{10}{33}$ .

(D) The probability that both balls are green is $\frac{5}{11}$ .

Choose the correct answer from the options given below:

2026: 30 May Shift 1

In a deck of lotteries, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting prize?

A basket contains 4 red, 5 blue and 3 green marbles. If three marbles are picked up at random, what is the probability that at least one is blue?

Solution

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