Question

One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 7. (Round answer to four decimals.)

Answer 1

A deck of Cards will have 52 Cards.

52 Cards will have 4 designs i.e Heartin, Diamond, Spade and Claver. Two Colours i.e Red and Black. Numbes from 2, to 10. and Alphabets J,Q,K,A

Heartin ( Red Colour ): 2, 3, 4, 5, 6, ,7, 8, 9, 10, J, Q, K, A ---- 13 Cards

Diamond ( Red Colour ) : 2, 3, 4, 5, 6, ,7, 8, 9, 10, J, Q, K, A ---- 13 Cards.

Spade ( Black Colour ) : 2, 3, 4, 5, 6, ,7, 8, 9, 10, J, Q, K, A ---- 13 Cards

Claver (Black Colour): 2, 3, 4, 5, 6, ,7, 8, 9, 10, J, Q, K, A ---- 13 Cards

Therefore We have 13 Diamond Cards and the number Cards Less than 7 are 2, 3, 4, 5, 6 in each desing i.e we have 20 number of cards ( 2, 3, 4, 5, 6 )x 4 = Cards.

2, 3, 4, 5, 6 in Diamond

2, 3, 4, 5, 6 in Heartin

2, 3, 4, 5, 6 in Spade

2, 3, 4, 5, 6 in Claver.

We know thatNo

Where m = Favourable Number of Events

n = Total number of Events.

Now the way of drawing one card from 52 cards is

m = Diamond Or a Card less tha 7

Let Diamond Card = A

Card Less than 7 = B

NOTE; In Probability the word "Or" refers to ADDITION.

m = The way of drawing a Diamond Card from 13 Diamond Cards + The way of drawing one card Less than 7 from 20 Cards Less than 7 - Drawing a cards Less than 7 which is in Diamond (i.e Intersection of Less than 7 card and Diamond Card )