
A bag contains red, black and white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is: red or white.
Answer
432.3k+ views
Hint: The formula that is needed to find the probability is
,
where is no. of favorable outcome and is total no. of events in the sample space.
The probability of two disjoint events or is given by
Complete step by step answer:
It is given that the bag contains red, black and white balls.
Then the sample space is
Therefore, the total number of balls in the bag is
That is, the total no. of event in the sample
To find: Probability of getting a red or white ball.
Let be the event of getting a red ball, then the probability of getting a red ball is given by
,
where is no. of favorable outcome and is total no. of events in the sample space.
From the sample space we get,
Therefore,
Let be the event of getting a white ball, then the probability of getting a white ball is given by
,
where is no. of favorable outcome and is total no. of events in the sample space.
Again, from the sample space we get,
Therefore,
Let be the event of getting a red or white ball, then the probability of is given by
Therefore,
Simplifying this we will get,
Thus, the probability of getting a red or white ball is
Note: In this problem both the events are disjoints that is event of getting red ball and event of getting white ball are disjoint event (i.e. There is no intersection between these two events) so we used the formula . If the events are not disjoint events, then we have to use the formula where is intersection between the events and .
where
The probability of two disjoint events
Complete step by step answer:
It is given that the bag contains
Then the sample space is
Therefore, the total number of balls in the bag is
That is, the total no. of event in the sample
To find: Probability of getting a red or white ball.
Let
where
From the sample space we get,
Therefore,
Let
where
Again, from the sample space we get,
Therefore,
Let
Therefore,
Simplifying this we will get,
Thus, the probability of getting a red or white ball is
Note: In this problem both the events are disjoints that is event of getting red ball and event of getting white ball are disjoint event (i.e. There is no intersection between these two events) so we used the formula
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