Answer
Verified
417k+ views
Hint- In this problem we are rolling up a dice and tossing a coin simultaneously. We have to find the probability of getting a head and an odd number, so write all the possible sample cases that the event of rolling a dice and throwing up a coin can have. Amongst these all possible events just take out the one with an odd number and head. Then use the basic probability formula to reach the answer.
Complete step-by-step answer:
Let ${\text{E}}$ be the event of getting a head and an odd number after rolling up a dice and throwing up a coin simultaneously.
So total possible sample points for event E will be (1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T).
Thus ${\text{n(S) = 12}}$……………………… (1)
Now the favorable cases for event E will be the one having head and an odd number, so they are (1, H), (3, H), (5, H).
Thus ${\text{n(E) = 3}}$…………………….. (2)
Now using the basic formula of probability that probability of an event A is ${\text{P(A) = }}\dfrac{{{\text{favorable outcomes}}}}{{{\text{total number of outcomes}}}} = \dfrac{{{\text{n(A)}}}}{{{\text{n(S)}}}}$………………………… (3)
So probability of event E will be${\text{P(E)}}$, using equation (1)
${\text{P}}\left( {\text{E}} \right) = \dfrac{{{\text{n(E)}}}}{{{\text{n(S)}}}}$………………… (4)
On substituting the values from equation (1) and (2) we get,
${\text{P}}\left( {\text{E}} \right) = \dfrac{3}{{12}} = \dfrac{1}{4}$
So the probability of getting a head and an odd number after rolling up a dice and throwing up a coin simultaneously is $\dfrac{1}{4}$.
Thus option (b) is the right answer.
Note – Whenever we face such types of problems the key concept is to have the understanding of the basic probability formula. This along with the all possible sample cases with the favorable cases as per the question requirement will help us to get the answer.
Complete step-by-step answer:
Let ${\text{E}}$ be the event of getting a head and an odd number after rolling up a dice and throwing up a coin simultaneously.
So total possible sample points for event E will be (1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T).
Thus ${\text{n(S) = 12}}$……………………… (1)
Now the favorable cases for event E will be the one having head and an odd number, so they are (1, H), (3, H), (5, H).
Thus ${\text{n(E) = 3}}$…………………….. (2)
Now using the basic formula of probability that probability of an event A is ${\text{P(A) = }}\dfrac{{{\text{favorable outcomes}}}}{{{\text{total number of outcomes}}}} = \dfrac{{{\text{n(A)}}}}{{{\text{n(S)}}}}$………………………… (3)
So probability of event E will be${\text{P(E)}}$, using equation (1)
${\text{P}}\left( {\text{E}} \right) = \dfrac{{{\text{n(E)}}}}{{{\text{n(S)}}}}$………………… (4)
On substituting the values from equation (1) and (2) we get,
${\text{P}}\left( {\text{E}} \right) = \dfrac{3}{{12}} = \dfrac{1}{4}$
So the probability of getting a head and an odd number after rolling up a dice and throwing up a coin simultaneously is $\dfrac{1}{4}$.
Thus option (b) is the right answer.
Note – Whenever we face such types of problems the key concept is to have the understanding of the basic probability formula. This along with the all possible sample cases with the favorable cases as per the question requirement will help us to get the answer.
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
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE