Question

Find the probability of selecting a red card or a 4 from a deck of 52 cards.A.7/13B.15/26C.6/13D.3/5

Answer 1

The probabilityIna deck of 52 cards, there are 26 red cards and 4 cards numbered 4.

Thus,

$\begin{gathered} \text{Number of red cards = n(red cards) =26} \\ \text{Number of 4 = n(4) = 4} \\ \text{Total number of cards in a deck = 52} \end{gathered}$

Probability of an event is evaluated as

$Pr\text{ = }\frac{\text{number of favourable outcomes}}{\text{total number of possible outcomes}}$

Thus,

$\begin{gathered} \text{Probability of picking a red card = Pr(R)=}\frac{\text{number of red cards}}{total\text{ number of cards}} \\ Pr(R\text{) = }\frac{\text{26}}{52}=\frac{1}{2} \\ \Rightarrow Pr(R\text{) = }\frac{1}{2} \end{gathered}$

Similarly,

$\begin{gathered} \text{Probability of picking a 4 = Pr(4) = }\frac{\text{total number of 4}}{total\text{ number of cards}} \\ Pr(4)=\frac{4}{52}\text{ = }\frac{1}{13} \\ \Rightarrow Pr(4_{_{}})=\text{ }\frac{1}{13} \end{gathered}$

The probability of selecting a red card or a 4 is evaluated as

$\begin{gathered} Pr(R\text{ }\cup\text{ 4) = Pr(R) + Pr(4) } \\ =\text{ }\frac{1}{2}\text{ + }\frac{1}{13} \\ \text{LCM = 26} \\ \Rightarrow\frac{13+2}{26}\text{ =}\frac{15}{26} \\ Pr(R\text{ }\cup\text{ 4)=}\frac{15}{26} \end{gathered}$

Thus, the probability of selecting a red card or a 4 from a deck of 52 cards is

$\frac{15}{26}$

The correct option is B