Question

An urn holds 13 identical balls except that 3 are white, 5 are black, and 5 are red. An experiment consists of selecting two balls in succession without replacement and observing the color of each of the balls.

How many outcomes are in the sample space for this experiment?


How many outcomes are in the event "no ball is white?"

Answer 1

The number of total possible outcomes also called the sample space of the experiment is 156.

The number of outcomes in 'no white ball' event is 56.

• White balls, W = 3
• Black balls, B = 5
• Red balls, R = 5

Since selection is performed without replacement :

• Total number of possible outcomes on first pick = 13
• Total number of possible outcomes on second pick = 13 - 1 = 12
• Number of outcomes in sample space = 13 × 12 = 156 outcomes.

Probability that no ball is white ::

No white on first pick :

• P(No white) = (R + B) ÷ Total = 8 / 13

No white on second pick :

• P(No white) = 7 / 12

Probability of not picking a white ball :

• (8/13 × 7/12) = 56/156

Number of outcomes in the event no white balls :

• P(not picking a white ball) × total possible outcomes
• (56/156) × 156 = 56 outcomes.

Therefore, the Number of outcomes in the sample space is 156 while the Number of outcomes in the event 'no white ball' is 56.

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