Question 7 Exercise 6.5

Solutions of Question 7 of Exercise 6.5 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

One card is drawn from pack of $52$ cards, what is the probability that the card drawn is neither red nor king?

A deck of playing cards consists of $52$ cards out of which $26$ are black cards.

Other $26$ are red cards, where red cards consists of $13$ cards of heart,

$13$ cards of diamond and black cards consists of $13$ cards of spades, $13$ cards are club.

$13$ cards in each suit are king, queen, Jack, $10,9,8,7,6,5,4,3$ and $2.$

Probability of red çard is: $$=\dfrac{13}{52}=\dfrac{1}{4}$$ Probability of king is: $$=\dfrac{4}{52}=\dfrac{1}{13}$$ Since the events are mutually disjoints therefore, by addition law of probability we have $$\begin{align} P(A \cup B)&=P(A)+P(B) \\ & =\dfrac{1}{4}+\dfrac{1}{13}=\dfrac{17}{52} \end{align}$$ Now the card should be neither red nor king so by complementary events,

we have that probability that it is neither red nor king is: $$=1-\dfrac{17}{52}=\dfrac{35}{52}$$

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