Answer
Verified
424.5k+ views
Hint: Use the fundamental definition of probability that it can be measured by ratio of number of favorable cases to total cases/ sample spaces.
Complete step-by-step answer:
Here, it is given that Box contains 4 white balls, 6 red balls, 7 black balls and 3 blue balls i.e. in total 20 balls are present in the box.
Hence, Total balls in Box = 20.
A. neither white nor black
Probability of drawing neither white nor black balls means drawing red balls or blue balls.
So, total probability of drawing Red balls or Blue balls = Probability of drawing Red balls +
Probability of drawing Blue balls.
Now, we know the definition of probability of an event can be given as
P(E)=Number of favorable cases/Total cases\[\ldots \ldots (1)\]
Hence, Probability of drawing Red balls or Blue balls=
$P=\dfrac{6}{20}+\dfrac{3}{20}=\dfrac{9}{20}$
Therefore, Probability of drawing neither white nor black be$\dfrac{9}{20}$.
B. Red or white
Probability of drawing either Red of White balls can be given as a summation of probability
of drawing Red Balls and white balls both.
Number of Red balls= 6
Number of white balls= 4
Total number of balls= 20
Now, from equation (1) , we can give required probability as
P=Probability of drawing Red balls + Probability of drawing white balls
Hence, we get
$P=\dfrac{6}{20}+\dfrac{4}{20}=\dfrac{10}{20}=\dfrac{1}{2}$
C. either white or red or black or blue
Here, we need to involve the probability of drawing each colour as we are drawing either of
all balls of any colour.
So, here probability of either white or red or black or blue can be given as
P= Probability of drawing (Red)+(White)+(Black)+(Blue)
As we have
Number of Red balls= 6
Number of White balls= 4
Number of black balls= 7
Number of blue balls= 3
Total balls=20
Hence,
$P=\dfrac{4}{20}+\dfrac{6}{20}+\dfrac{7}{20}+\dfrac{3}{20}=\dfrac{20}{20}=1$
Therefore, answers of the problem are $\dfrac{9}{20},\dfrac{1}{2},1.$
Note: One can miss any of the colour while writing the probability of drawing that colour. He/she may involve favourable cases of any other colour ball.
First case can also be calculated by getting the probability of either white or black balls then subtract it from 1 as $1-\dfrac{1}{20}=\dfrac{19}{20}$.
One can go wrong while writing probability of red or white (2nd case) or with the last part as well. One can multiply the probability of red and white balls to get probability of red or white which is the wrong approach. So, take care of it in these kinds of questions.
Complete step-by-step answer:
Here, it is given that Box contains 4 white balls, 6 red balls, 7 black balls and 3 blue balls i.e. in total 20 balls are present in the box.
Hence, Total balls in Box = 20.
A. neither white nor black
Probability of drawing neither white nor black balls means drawing red balls or blue balls.
So, total probability of drawing Red balls or Blue balls = Probability of drawing Red balls +
Probability of drawing Blue balls.
Now, we know the definition of probability of an event can be given as
P(E)=Number of favorable cases/Total cases\[\ldots \ldots (1)\]
Hence, Probability of drawing Red balls or Blue balls=
$P=\dfrac{6}{20}+\dfrac{3}{20}=\dfrac{9}{20}$
Therefore, Probability of drawing neither white nor black be$\dfrac{9}{20}$.
B. Red or white
Probability of drawing either Red of White balls can be given as a summation of probability
of drawing Red Balls and white balls both.
Number of Red balls= 6
Number of white balls= 4
Total number of balls= 20
Now, from equation (1) , we can give required probability as
P=Probability of drawing Red balls + Probability of drawing white balls
Hence, we get
$P=\dfrac{6}{20}+\dfrac{4}{20}=\dfrac{10}{20}=\dfrac{1}{2}$
C. either white or red or black or blue
Here, we need to involve the probability of drawing each colour as we are drawing either of
all balls of any colour.
So, here probability of either white or red or black or blue can be given as
P= Probability of drawing (Red)+(White)+(Black)+(Blue)
As we have
Number of Red balls= 6
Number of White balls= 4
Number of black balls= 7
Number of blue balls= 3
Total balls=20
Hence,
$P=\dfrac{4}{20}+\dfrac{6}{20}+\dfrac{7}{20}+\dfrac{3}{20}=\dfrac{20}{20}=1$
Therefore, answers of the problem are $\dfrac{9}{20},\dfrac{1}{2},1.$
Note: One can miss any of the colour while writing the probability of drawing that colour. He/she may involve favourable cases of any other colour ball.
First case can also be calculated by getting the probability of either white or black balls then subtract it from 1 as $1-\dfrac{1}{20}=\dfrac{19}{20}$.
One can go wrong while writing probability of red or white (2nd case) or with the last part as well. One can multiply the probability of red and white balls to get probability of red or white which is the wrong approach. So, take care of it in these kinds of questions.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Write an application to the principal requesting five class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Write a letter to the principal requesting him to grant class 10 english CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
Write two differences between autotrophic and heterotrophic class 10 biology CBSE
What is the past tense of the word hurt class 10 english CBSE