Question

A magician randomly draws a card from a deck of cards ( 52). On a scale of 1 to 3 ( 1 being most likely to happen, 2 being somewhat likely to happen, and 3 being least likely to happen).  Show all steps. Drawing a 3. Drawing any black card. Drawing a King or Queen.

Answer 1

Solution:

Given: A magician randomly draws a card from a deck of cards ( 52).

On a scale of 1 to 3 ( 1 being most likely to happen, 2 being somewhat likely to happen, and 3 being least likely to happen)

Part a) Drawing a 3

Find :

P(  Drawing a 3) =.........?

there are 4 cards of number 3 ,

thus we can select any one card out of 4 cards of number 3.

thus number of ways selecting a number 3 card from 4 cards= 4 ways

and number of ways of drawing any one card out of 52 playing cards = 52 ways

thus

P(  Drawing a 3) = 4/52

P(  Drawing a 3) = 1/13

P(  Drawing a 3) = 0.019231

Since this probability is very close to 0, hence drawing a 3 is least likely to happen. thus

Drawing a 3 :   3 (being least likely to happen).

Part ii) Drawing any black card.

P(  Drawing any black card) =.........?

there is 26 black cards, hence:

P(  Drawing any black card) = 26 / 52

P(  Drawing any black card) = 0.5

this probability is high, hence  

Drawing any black card: 1 ( being most likely to happen)

Part iii) Drawing a King or Queen.

P( Drawing a King or Queen) =...........?

there are 4 king cards and 4 queen cards

thus

P(Drawing a King or Queen) = 4/52 + 4/52

P(Drawing a King or Queen) = 8/52

P(Drawing a King or Queen) = 0.153846

Since this probability neither too low or too high, thus

Drawing a King or Queen: 2 (being somewhat likely to happen)