Probability, Quantitative Aptitude Subject

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17.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

(a)1/2

(b)2/5

(d)9/20

Answer!

Answer is: DHere, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.

18.

bag contains 3 blue balls, 4 green balls and 5 red balls. Three balls are drawn simultaneously at random. Find the probability that two are blue and one is green?

(a)3/55

(b)5/22

(d)8/10

Answer!

Answer is: AThere balls can be drawn from 12 balls in ¹²C₃ ways.
Two balls blue and one green ball can be drawn in ³C₂.⁴C₁ ways.
âˆ´ The required probability = ³C₂. ⁴C₁/¹²C₃ = 3/55.

19.

A bag contains 3 blue balls, 4 green balls and 5 red balls. Three balls are drawn simultaneously at random. Find the probability that the balls are of the same color.

(a)4/12

(b)3/44

(d)6/ 33

Answer!

Answer is: BThree balls can be drawn from 12 balls in ¹²C₃ ways.
3 blue balls or 3 green balls or 3 red balls can be drawn in ³C₃ or ⁴C₃ or ⁵C₃ ways required probability = ³C₃ + ⁴C₃ + ⁵C₃/ ¹²C₃ = 3/44.

20.

Mohan had 5 fifty rupee notes, 3 hundred rupee notes and 4 five hundred rupee notes in his pocket. Two notes were drawn at random. Find the odds in favor of both being fifty rupee notes.

(a)5/33

(b)5/28

(d)10/54

Answer!

Answer is: BTotal number of ways of drawing two notes from the pocket containing 12 notes is ¹²C₂ ways.
The number of ways in which two fifty rupee notes can be draw = ⁵C₂.
The probability of choosing two fifty rupee notes = ⁵C₂/¹²C₂ = 5/33.
âˆ´ Odds in favor of the event = favorable ways : unfavorable ways = 5/28.

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