A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $12$.
A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $12$.
since the fair coin has $1$ marked on one face and $6$ on the other, and the die has six faces that are numbered $1,\,2,\,3\,,4,\,5,$ and $6,$ the sample space is given by
$S =\{(1,1),(1,2),(1,3),(1,4)$, $(1,5),(1,6),(6,1)$, $(6,2),(6,3),(6,4),(6,5),(6,6)\}$
Accordingly, $n ( S )=12$
Let $B$ be the event in which the sum of numbers that turn up is $12.$
Accordingly, $B=\{(6,6)\}$
$\therefore P(B)=\frac{\text { Number of outcomes favourable to } B}{\text { Total number of possible outcomes }}=\frac{n(B)}{n(S)}=\frac{1}{12}$
Similar Questions
In order to get at least once a head with probability $ \ge 0.9,$ the number of times a coin needs to be tossed is
In order to get at least once a head with probability $ \ge 0.9,$ the number of times a coin needs to be tossed is
Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3…., 6$, the probability of the face marked $K$ turning up when die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to
Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3…., 6$, the probability of the face marked $K$ turning up when die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to
Two dice are thrown simultaneously. The probability of getting the sum $2$ or $8$ or $12$ is
Two dice are thrown simultaneously. The probability of getting the sum $2$ or $8$ or $12$ is
The corners of regular tetrahedrons are numbered $1, 2, 3, 4.$ Three tetrahedrons are tossed. The probability that the sum of upward corners will be $5$ is
The corners of regular tetrahedrons are numbered $1, 2, 3, 4.$ Three tetrahedrons are tossed. The probability that the sum of upward corners will be $5$ is
A coin is tossed three times, consider the following events.
$A: $ ' No head appears ', $B:$ ' Exactly one head appears ' and $C:$ ' Atleast two heads appear '
Do they form a set of mutually exclusive and exhaustive events?
A coin is tossed three times, consider the following events.
$A: $ ' No head appears ', $B:$ ' Exactly one head appears ' and $C:$ ' Atleast two heads appear '
Do they form a set of mutually exclusive and exhaustive events?