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

Answer:

0.72

Step-by-step 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 = $\frac{13}{50}$

When 1 spade card is lost

So, No. of spade cards = 12

Total cards = 50

So, probability of getting spade = $\frac{12}{50}$

When 2 spade cards are lost

So, No. of spade cards = 11

Total cards = 50

So, probability of getting spade = $\frac{11}{50}$

So, The he probability that a random card drawn from this (defective) deck is a spade =  $\frac{13}{50}+\frac{12}{50}+\frac{11}{50}$

                  =  $\frac{36}{50}$

                  =  [tex]0.72/tex]

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