Question

Wesley draws a card at random from a well-shuffled deck of playing cards.

Answer 1

Answer:

The probability that Wesley draws an ace or a jack is:

$\frac{8}{52}$

The probability that Wesley draws a number card or a black card is :

$\frac{44}{52}$

Step-by-step explanation:

Total no. of playing cards = 52

No. of diamond cards (red colour )= 13

No. of heart cards(red colour)=13

No. of spade cards (black colour)=13

No. of club cards (black colour )=13

No. of kings = 4 (1 diamond [red], 1 spade [black],1 heart[red],1club[black])

No. of queens = 4 (1 diamond [red], 1 spade [black],1 heart[red],1club[black])

No. of jacks  = 4 (1 diamond [red], 1 spade [black],1 heart[red],1club[black])

No. of ace = 4 (1 diamond [red], 1 spade [black],1 heart[red],1club[black])

Number cards in diamond[red colour] = {2,3,4,5,6,7,8,9,10}=9

Number cards in heart[red colour] = {2,3,4,5,6,7,8,9,10}=9

Number cards in spade[black colour] = {2,3,4,5,6,7,8,9,10}=9

Number cards in club[black colour] = {2,3,4,5,6,7,8,9,10}=9

Thus total number cards = 9+9+9+9 =36

The probability that wesley draws an ace or a jack

Since no. of ace card = 4

No. jack card = 4

Total of ace and jack cards = 8

Thus probability that wesley draws an ace or a jack = no.of ace card +no. of jack cards / total no. of cards

⇒$\frac{8}{52}$

Now The probability that Wesley draws a number card or a black card

Since no. cards = 36 (including black number cards )

Remaining black cards = 1 king of spade , 1 queen of spade , 1 ace of spade , 1  jack of spade , 1 king of club , 1 queen of club , 1 ace of clun , 1 jack of club = 8 cards

no. cards +remaining black cards = 36+8=44

Thus The probability that Wesley draws a number card or a black card =

no. cards + black cards / total cards :

⇒$\frac{44}{52}$

Hence The probability that Wesley draws an ace or a jack is:

$\frac{8}{52}$

The probability that Wesley draws a number card or a black card is :

$\frac{44}{52}$

Answer 2

8/52 for the first one and 9/26 for the second