Question

As shown above a classical deck of card is made up 52 cards suppose one card is selected at random and calculate the following proper ability

Answer 1

To determine the probability of selecting a classical deck of card

(a) Probability of selecting a 7 or club

`\begin{gathered} Pr(\text{selecting a 7 or club) = pr( selecting a 7) + pr(selecting a club )} \\ \text{pr( selecting a 7) = }(4)/(52) \\ \text{pr( selecting a club) = }(13)/(52) \\ Pr(\text{selecting a 7 or club) = }(4)/(52)+(13)/(52)=\text{ }(4+13)/(52)=(17)/(52)\text{ = 0.3269} \\ Pr(\text{selecting a 7 or club) = }0.327\text{ (3dp)} \end{gathered}`

(b) Probability of selecting a face card or heart

`\begin{gathered} Pr(\text{selecting a face card or heart) = pr(selecting a face card) + pr(selecting a heart)} \\ Pr(\text{selecting a face card) = }(12)/(52) \\ Pr(\text{selecting a heart) = }(13)/(52) \\ Pr(\text{selecting a face card or heart) = }(12)/(52)+(13)/(52)=(12+13)/(52)=(25)/(52)=0.4807 \\ Pr(\text{selecting a face card or heart) }=\text{ 0.481 (3dp)} \end{gathered}`

(c) Probability of selecting both a face card and a club

`\begin{gathered} Pr(\text{selecting both a face card and a club) = pr(selecting a face card)+pr(selecting a club)} \\ \text{pr(selecting a face card) = }(12)/(52) \\ \text{pr(selecting a club) = }(13)/(52) \\ Pr(\text{selecting both a face card and a club) = }(12)/(52)\text{ }*(13)/(52)=\text{ }(3)/(52)=0.0577 \\ Pr(\text{selecting both a face card and a club) = 0.058 (3dp)} \end{gathered}`