Question

Consider a standard deck of 52 cards with 4 suits. Define events! a. Suppose you pick 1 card at random from the deck. What is the probability that card is a heart? b. Suppose you pick one card from the deck. What is the probability that card is a 5? c. Suppose you pick one card from the deck. What is the probability that the card is a heart and a 5? d. Suppose you pick one card from the deck. What is the probability that the card is a heart or a 5? these two events independent? Explain why or why not using mathematics. e. Are f What is the complement of drawing a 57

Answer 1

Consider a standard deck of 52 cards with 4 suits.

(a) 1 card is picked at random from the deck.What is the probability that the card is a heart ?

In a standard deck,there are 13 hearts.

All possible cases of drawing one card at random is (52 C 1).

Favourable cases is (13 C 1)

So,required Probability

=(13 C 1)/(52 C 1)

=13/52

=1/4

=0.25

(b)

One card is picked from the deck.What is the probability that the card is a 5?

In a standard deck,there are 4 denominations of 5.

So,favourable cases = (4 C 1)

So,required probability

=(4 C 1)/(52 C 1)

=4/52

=1/13

=0.076

(c)

One card is picked from the deck.What is the probability that the card is a heart and a 5?

In a deck,there is only one case where denomination belongs to the heart suit.

So,favourable cases=1

so,required probability

=1/(52 C 1)

=1/52

=0.019

(d)

One card is picked from the deck.What is the probability that the card is a heart or a 5?

P(card is heart or a 5)

=P(card is heart)+P(card is 5)-P(card is heart and 5)

=0.25+0.076-0.019

=0.307

(e)

P(card is heart)

=0.25

P(card is 5)

=0.076

P(card is heart and 5)

=0.019

And

P(card is heart)P(card is 5)

=0.25*0.076

=0.019

So,as P(card is heart and 5)=P(card is heart)*P(card is 5),

the events that the card is a heart and the card is a 5, are mutually independent.

(f)

P(complement of drawing a 5)

=1-P(card is a 5)

=1-0.076

=0.0.924