Probability Question

Question

 A) A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the card is neither a spade nor a Jack?      

B) Six friends Aisha, Bilal, Kamran, Danish, Emaan and Farukh want to sit in a row at the cinema. If there are only six seats available, how many ways can we seat these friends?

Answer 1

A) total number of cards = 52

total number of spades in 52 cards =13 = 12 cards +1 jack card

total number of jacks in 52 cards = 4

total number of cards which are neither spades nor shades=13+3=16

total number of cards which are neither a spade and neither a jack = 52 -16 = 36

the probability that the taken card is neither a spade nor a jack = favorable cases / total cases

= 36 / 52

= 9 / 13

B) the total number of seats = 6

the total number of persons = 6

1st seat can be occupied by any one of the 6 persons so 6 possible ways for 1st seat

2nd seat can be occupied by any one of the 5 persons so 5 possible ways for 2nd seat

3rd seat can be occupied by any one of the 4 persons so 4 possible ways for 3rd seat

4th seat can be occupied by any one of the 3 persons so 3 possible ways for 4th seat

5th seat can be occupied by any one of the 2 persons so 2 possible ways for 5thseat

6th seat can be occupied by any one of the 1 persons so 1 possible way for 6th seat

so total number of ways = 6 * 5* 4* 3 * 2 * 1 = 720 ways

Answer 2

52 cards; 4 suits; 13cards/suit.

13spades+3more jacks=16cards.

odds=36:16