# A dice is rolled and a coin is tossed simultaneously. What is the probability of getting a head and an odd number?

$

(a){\text{ }}\dfrac{1}{3} \\

(a){\text{ }}\dfrac{1}{4} \\

(a){\text{ }}\dfrac{1}{2} \\

(a){\text{ }}\dfrac{2}{3} \\

$

Last updated date: 16th Mar 2023

•

Total views: 305.4k

•

Views today: 2.84k

Answer

Verified

305.4k+ 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

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE