A fair coin with 1 marked on one face and 6 o | vedclass

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(A) The fair coin has faces marked $1$ and $6$. The fair die has faces marked $1, 2, 3, 4, 5,$ and $6$.The sample space $S$ is the set of all possible

Vedclass · Accepted Answer

$\frac{1}{12}$

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(A) The fair coin has faces marked $1$ and $6$. The fair die has faces marked $1, 2, 3, 4, 5,$ and $6$.The sample space $S$ is the set of all possible ordered pairs $(c, d)$,where $c$ is the coin result and $d$ is the die result:$S = \{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$The total number of outcomes is $n(S) = 12$.Let $A$ be the event that the sum of the numbers is $3$. Looking at the sample space,the only outcome where the sum is $3$ is $(1, 2)$.Thus,$A = \{(1, 2)\}$ and $n(A) = 1$.The probability $P(A)$ is given by:$P(A) = \frac{n(A)}{n(S)} = \frac{1}{12}$

$A$ 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 $3$.

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