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What is the probability of getting a non red ball from a bag containing 4 Red 5 blue and 3 black balls?

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  • Last Updated : 24 Jan, 2022

Probability is the likelihood of occurrence of the desired outcome(result) over the set of all possible outcomes (results) of a situation. Probability in simple terms indicates possibility. The probability of occurrence of an event denotes the ratio of the desired result to all possible results.

Terms in probability

There are different terms often used in probability. Terms like an experiment, trial, event, mutually exclusive events, outcome, favorable event, etc. Let’s take a look at them in detail,

  • Experiment: Experiment refers to any kind of activity with non-defined results.
  • Trial: Trial refers to the different attempts of an experiment
  • Event: Event refers to a trial with a well-defined outcome
  • Mutually Exclusive Events: Mutually Exclusive Events are events that have nothing in common, and the occurrence of one event prevents the occurrence of another.
  • Outcome: Outcome refers to the final result of trial
  • Favorable Event: Favorable Events are the events with the desired outcome/result

Probability of occurrence of any event

The formal definition of the probability of occurrence of any event would be, Probability of occurrence of Favorable Event/ Probability of Occurrence of All Events (Favorable + Unfavorable). The total set of events in an event of probability is the sum of Favorable Events and Unfavorable Events. These tend to be the denominator of the Probability calculation ratio

The probability of getting a non red ball from a bag containing 4 Red 5 blue and 3 black balls

Solution:

figure 1: Bag containing the balls

Number of red balls in the bag = 4

Number of blue balls in the bag = 5 

Number of black balls in the bag = 3

Total balls in the bag = 4 + 5 + 3 = 12

Probability of getting a red ball 

= Red Balls in the bag/ Total number of Balls in the bag 

= 4/12 

Probability of getting a blue ball 

= Blue Balls in the bag/ Total number of Balls in the bag 

= 5/12

Probability of getting a black ball

= Black Balls in the bag/ Total number of Balls in the bag 

= 3/12

Now, the Probability of getting a non-red ball can be calculated by three ways:

1st Way:

Probability of getting a non-red ball 

= 1 – Probability of getting a red ball 

= 1- 4/12

= 8/12

2nd Way:

Probability of getting a non-red ball 

= Sum of Probabilities of getting either a Blue ball or a black ball

= Probability of getting a blue ball + Probability of getting a black ball

= 5/12 + 3/12

= 8/12

3rd Way:

Probability of getting a non-red ball 

= (Blue Balls in the bag + Black Balls in the bag) / Total number of Balls in the bag 

= (5 + 3)/12

= 8/12

Either of the three ways fetches the same result: 8/12 to the above problem.

Similar Problems

Question 1: The probability of getting a red ball from a bag containing 6 Red and 4 black balls

Solution:

No of red balls in the bag = 6

No of black balls in the bag = 4

Total balls in the bag = 6 + 4 = 10

Probability of getting a red ball

= Red Balls in the bag/ Total number of Balls in the bag

= 6/10 

Question 2: The probability of getting a King from a deck of cards.

Solution:

Kings in the Deck = 4

Total No. of cards in the deck = 52

Probability of occurrence of a King from a deck of cards

= Kings in the Deck /  Total No. of cards in the deck

= 4/52 

Question 3: The probability of getting a non blue ball from a bag containing 3 Red 3 blue and 4 black balls.

Solution:

No of red balls in the bag = 3

No of blue balls in the bag = 3

No of black balls in the bag = 4

Total balls in the bag= 3 + 3 + 4

Probability of getting a red ball

= Red Balls in the bag/ Total number of Balls in the bag

= 3/10

Probability of getting a blue ball

= Blue Balls in the bag/ Total number of Balls in the bag

= 3/10

Probability of getting a black ball

= Black Balls in the bag/ Total no. of Balls in the bag

= 4/10

Probability of getting a non-blue ball

= 1 – Probability of getting a blue ball

= 1 – 3/10

= 7/10

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