Solution: Probability refers to a result's chance or potential. It describes the likelihood of a specific occurrence. Given: A dice is thrown once Required to find: Prime numbers on a dice are 2, 3, and 5. So, the total number of prime numbers is 3. We know that, Probability = Number of favourable outcomes/ Total number of outcomes Thus, probability of getting a prime number = 3/6 = 1/2 A coin and a dice are thrown together. Find the probability of getting (a) a...A coin and a dice are thrown together. Find the probability of getting
(a) a tail and a two
B. A head and a score greater than 4
C. A head and a prime number? To get notifications when anyone posts a new answer to this question,
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If a die and a coin are thrown together, what is the probability of getting 6 and heads?
Answer Verified
Hint:
Here, we are asked to find the probability of getting head on coin and number 6 on die.
So, firstly, we will write down all the possible outcomes in the sample space.
Thus, count the number of outcomes in the sample space.
Let X be the event getting head on coin and number 6 on die.
Then, check how much the number of outcomes is favourable to the given event X.
Hence, find the probability of the given event using the formula $P\left( X \right) =
\dfrac{{Number\,of\,outcomes\,favourable\,to\,the\,given\,event}}{{Total\,number\,of\,outcomes\,in\,the\,sample\,space}}$ . Complete step by step solution:
The given events are throwing of a dice and tossing of a coin.
Let, H be the event where the coin shows head and T is the event where the coin shows tail.
Now, the sample space for the given events can be written as $S = \left\{ {\left( {1,H} \right),\left( {2,H} \right),\left( {3,H} \right),\left( {4,H} \right),\left( {5,H}
\right),\left( {6,H} \right),\left( {1,T} \right),\left( {2,T} \right),\left( {3,T} \right),\left( {4,T} \right),\left( {5,T} \right),\left( {6,T} \right)} \right\}$
Therefore, the total number of outcomes \[n\left( S \right) = 12\] .
Now, we are asked to find the probability of the coin showing head and the die showing 6 simultaneously.
Let X be the event that the coin shows head and the die shows 6.
Now, the total number of outcomes favourable to the event X is 1 which is 6
appears on die and head appears on coin i.e. $\left( {6,H} \right)$ .
$\therefore n\left( X \right) = 1$
Thus, the probability of getting head and 6 is $P\left( X \right) = \dfrac{{Number\,of\,outcomes\,favourable\,to\,the\,given\,event}}{{Total\,number\,of\,outcomes\,in\,the\,sample\,space}}$ .
$\therefore P\left( X \right) = \dfrac{{n\left( X \right)}}{{n\left( S \right)}}$
$\therefore P\left( X \right) = \dfrac{1}{{12}}$ Hence, the probability of
getting number 6 on die and head on coin is $\dfrac{1}{{12}}$. Note:
Alternate method:
Let X be the probability of getting number 6 on the die.
We know that the probability of getting any one of the numbers of die on throwing is $\dfrac{1}{6}$.
So, here $P\left( X \right) = \dfrac{1}{6}$.
Let H be the event that the coin shows heads.
Also, we know that the probability of getting a head on the coin when it is tossed is $\dfrac{1}{2}$.
So, we get $P\left( H
\right) = \dfrac{1}{2}$.
Now, let A be the probability that the above events occur simultaneously.
So, to get the probability of the event A occurring can be given by the product of the occurrence of the individual events X and H.
$\therefore P\left( A \right) = P\left( X \right) \cdot P\left( H \right)$
$
= \dfrac{1}{6} \times \dfrac{1}{2} \\
= \dfrac{1}{{12}}
$
Thus, the probability of getting number 6 on die and head
on coin is $\dfrac{1}{{12}}$.
What is the probability of getting a prime number in tossing a coin?
Hence the probability of getting a prime number is 1/2.
What is the probability of tossing a 6 on die and a head on a coin?
Thus, the probability of getting number 6 on die and head on coin is 112.
What is the probability of getting a tail on the coin and a prime number on the die?
Therefore, the probability of the event that 'tail' and a prime number turn up is 1/4.
How many outcomes are there in getting a prime number and a head when a die is rolled and a coin is tossed?
When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.
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