Getting an odd number and a tail when a die is rolled and a coin is tossed simultaneously

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} \\ $

Answer

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.

Which of the following arguments are correct and which are not correct? Give reasons for your answer. (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2

Solution:

We use the basic concepts of probability to find the required outcomes.

(i) Incorrect

If two coins are tossed simultaneously then,

Total possible outcomes are (H, H), (T, T), (H, T), (T, H) = 4

Number of outcomes to get two heads = (H, H) = 1

Number of outcomes to get two tails = (T, T) = 1

Number of outcomes to get any one of each = (H, T), (T, H) = 2

probability of getting two heads = Number of possible outcomes/Total number of favourable outcomes

= 1/4

probability of getting two tails = Number of possible outcomes/Total number of favourable outcomes

= 1/4

probability of getting one of each = Number of possible outcomes/Total number of favourable outcomes

= 2/4 = 1/2

It can be observed that the probability of each of the outcomes is not 1/3.

(ii) Correct

Total number of possible outcomes when a die is thrown = (1, 2, 3, 4, 5, 6)

Number of possible outcomes to get an odd number (1, 3, 5) = 3

Number of possible outcomes to get an even number (2, 4, 6) = 3

probability of getting odd number = Number of possible outcomes/Number of favourable outcomes

= 3/6 = 1/2

Thus, the probability of getting an odd number is 1/2.

Check out more about terms of probability.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 15

Video Solution:

Which of the following arguments are correct and which are not correct? Give reasons for your answer. (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 25

Summary:

The argument (i) If two coins are tossed simultaneously there are three possible outcomes—two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3 is incorrect and the argument (ii) If a die is thrown, there are two possible outcomes—an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.is correct

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