Concept of “Probability”-01

Question: A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow? [Ans. (3) 7/22 ]

(1) 5/33  (2) 5/22  (3) 7/22  (4) 7/33  (5) 7/66   

Solution:

Concept:

Probability: Probability of an event is defined as the ratio of no. of favorable cases to the no. of all possible outcomes. In other words, it is the ratio of n (E) and n (S).

P (E) = n (E)/n (S)

(1) 0 < P (E) < 1

(2) P (E) + P (E^’) = 1

Detailed Explanation: A bag contains 7 blue balls and 5 yellow balls. Here, total number of balls is 7+5 = 12, out of which two balls are to be selected at random. So, total no. of outcomes is ¹²C_2.

Since none of the two balls drawn should be yellow, this means, both should be blue. Total no. of blue balls is 7. So, no. of combinations is ⁷C₂.

Therefore, probability can be find out as

                            ⁷C₂      7×6       7

Probability = ------ = ------- = ------      Ans.

                           ¹²C₂     12×11   22

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