Question

5. Meredith is playing a game of solitaire, using a well-shuffled deck of 52 cards. If she lays out 7 cards face-up, determine the probability that they will all be spades. (2 marks)

Answer 1

$\text{Probability of an event = }\frac{Number\text{ of required outcome}}{Number\text{ of possible outcome}}$

Given that there are 52 well-shuffled cards and number of spades = 13, the probability of a picking a spade is evaluated as

$\begin{gathered} Pr(\text{spade) = }\frac{\text{13}}{52} \\ \Rightarrow Pr(spade)=\frac{1}{4} \end{gathered}$

When two or more events occur simultaneously, the probability of their occurrence is expressed as the multiplication of their individual probabilities.

Thus, when all 7 cards drawn are spades, the probability is evaluated as

$\begin{gathered} Pr(7\text{ spade) = }\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4} \\ =\frac{1}{16384} \end{gathered}$

Hence, the probability that they will all be spades is

$\frac{1}{16384}$