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

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

(b) Probability of selecting a face card or heart

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

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

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