Name: Algebra of Probability - Union and Intersection
Uploaded: 2019-07-19
Duration: 11 min 19 s
Description: In this video, let's learn the meaning of union and intersection of events and how to calculate their probabilities and practice some examples.

Question

On a walk Paul counts $70$ rabbits. Of these rabbits, $42$ are female, $34$ are not eating carrots, and $23$ are female and not eating carrots.

Draw a Venn diagram and hence find the number that are both female and eating carrots.

Find the probability that a rabbit is male and not eating carrots.

Accepted Answer

Let $n (U)$ $34$ Number of rabbits $23$

$n (A) =$ Number of female rabbits $= 42$

Number of male rabbits $= n (A^{'}) = n (U) - n (A) = 70 - 42 = 28$

$n (B) =$ Number of rabbits not eating carrots $= 34$

$n (A \cap B) =$ Number of rabbits both female and not eating carrots $= 23$

Number of female rabbits eating carrots $= n (A - B) = n (A) - n (A \cap B) = 42 - 23 = 19$

Number of rabbits that are not female i.e., male and eating carrots $= n {(A \cup B)}^{'} = n (U) - n (A \cup B)$

We know that, $n (A \cup B) = n (A) + n (B) - n (A \cap B)$

$\Rightarrow n (A \cup B) = 42 + 34 - 23 = 53$

Therefore, number of rabbits that are not female i.e., male and eating carrots $= n (A \cup B)^{'} = n (U) - n (A \cup B) = 70 - 53 = 17$

Drawing a Venn diagram for obtained data,

Number of male rabbits not eating carrots $= n (B - A) = n (B) - n (A \cap B) = 34 - 23 = 11$

Sample space $=$ Total number of rabbits $= 70$

Number of favourable outcomes $=$ Number of male rabbits and not eating carrots $= 11$

Probability of an event, $P (A) = \frac{Number of favourable outcomes of the event}{Sample space} = \frac{n (A)}{n (S)}$ .

Therefore, probability that a rabbit is male and not eating carrots $= \frac{11}{70}$

On a walk Paul counts $70$ rabbits. Of these rabbits, $42$ are female, $34$ are not eating carrots, and $23$ are female and not eating carrots.

Draw a Venn diagram and hence find the number that are both female and eating carrots.

Find the probability that a rabbit is male and not eating carrots.

Important Questions on Quantifying Randomness: Probability

Learn and Prepare for any exam you want !

On a walk Paul counts 70 rabbits. Of these rabbits, 42 are female, 34 are not eating carrots, and 23 are female and not eating carrots. Draw a Venn diagram and hence find the number that are both female and eating carrots. Find the probability that a rabbit is male and not eating carrots.

Important Questions on Quantifying Randomness: Probability

Learn and Prepare for any exam you want !

On a walk Paul counts $70$ rabbits. Of these rabbits, $42$ are female, $34$ are not eating carrots, and $23$ are female and not eating carrots.

Draw a Venn diagram and hence find the number that are both female and eating carrots.

Find the probability that a rabbit is male and not eating carrots.