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
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