Question

A card is drawn from a standard deck of fifty-two cards which have been well-shuffled seven times. What is the probability that the card is:

(a) Either a face card (jack,queen, king) or a ten?

(b) Either a spade or a face card?

Note* Both the logic and mathematical calculation must be shown in the answers.

Answer 1

A card is drawn from a standard deck of 52 cards, which have been well shuffled seven times.

Now, one card can be drawn from a 52 card deck in 52 ways.

So, number of all possible cases is 52.

(a)

We have to find the probability that the card drawn is either a face card, or a ten.

Now, each of the 4 suits contains one king, queen, jack, and ten.

So, there are 4*4, ie. 16 cards, which are either face cards, or ten.

So, number of favourable cases is 16.

So, required probability is

=16/52

=0.3077

So, the answer is 0.3077.

(b)

We have to find the probability that the card drawn is either a face card or a spade.

Now, in each suit, there are 3 face cards.

So, number of face cards is 4*3, ie. 12.

P(face card)=12/52.

Now, there are 13 spades in a deck.

So, P(spade)=13/52.

Again, there are 3 cards which are both spades, and face cards.

So, P(Face card and spade)=3/32.

Now, by addition theorem of probability, we see that

P(Face card or spade)

=P(Face card)+P(spade)-P(Face card and spade)

=12/52+13/52-3/52

=22/52

=0.4231

So, the probability that the card is either a face card or a spade is 0.4231.