Question

Michelle draws a card from a standard deck of 52 cards. She replaces the card and draws a second card. What is the probability that she draws a heart and then a spade?

A)



1
16



B)



1
26



C)



1
4



D)



1
52

 these are fractions

Answer 1

Option A.
`(1)/(16)`

Explanation:

Michelle draws a card from a standard deck of 52 cards.

It means sample taken n(S) = 52

When she draws a card which is a heart the favorable event n(E) = 13

Therefore probability of drawing a heart will be P1 =
`(n(E))/(n(S))=(13)/(52)=(1)/(4)`

She replaces this card and draws again. Therefore the probability of drawing second card which will be a spade will be P2 =
`(13)/(52)=(1)/(4)`

Now probability that she draws a heart and then a spade will be =
`P_(1).P_(2)=(1)/(4).(1)/(4)=(1)/(16)`

Option A.
`(1)/(16)` is the correct option.

Answer 2

The answer is A. The probability that you draw hearts than spades is 1/16 If drawing more than one card with replacement: The probability of drawing a specific card each time is 1/52n n= the number of draws. The probability of drawing a specific card each time is 1/13n. The probability of drawing a specific suit each time is 1/4n. Since you draw two types of cards,each time you drew is 1/4 so 1/4 times 1/4 is 1/16. Kind of cofusion right