Question

Two of the cards of an ordinary deck of 52 cards are lost. What is the probability that a random card drawn from this (defective) deck is a spade? (Show your work! Define any events that you use, and be clear and neat!)

Answer 1

0.72

Explanation:

Given :Two of the cards of an ordinary deck of 52 cards are lost.

To Find : What is the probability that a random card drawn from this (defective) deck is a spade?

Solution:

Total number of cards = 52

2 cards are lost

Remaining cards = 50

When no spade card is lost

So, No. of spade cards = 13

Total cards = 50

So, probability of getting spade =
`(13)/(50)`

When 1 spade card is lost

So, No. of spade cards = 12

Total cards = 50

So, probability of getting spade =
`(12)/(50)`

When 2 spade cards are lost

So, No. of spade cards = 11

Total cards = 50

So, probability of getting spade =
`(11)/(50)`

So, The he probability that a random card drawn from this (defective) deck is a spade =
`(13)/(50)+(12)/(50)+(11)/(50)`

=
`(36)/(50)`

= [tex]0.72/tex]

Hence the probability that a random card drawn from this (defective) deck is a spade is 0.72