Astreet magician asks a passerby to draw one card from a standard deck, remember it, and then replace it. the magician then shuffles the deck and asks the person to draw a second card. find the probability that at least one of the two cards was a heart.

P( At least one of the two cards was a heart)=7/16

Step-by-step explanation:

The solution to this question can be found in two ways.

First way: Since total number of heart in a deck are four,

Probability that neither of two cards had a heart is that at both times the card drawn was not a heart, since it is an independent event, thus probability both were not heart= ×

=

Thus, Probability that at least one of the two cards was a heart= 1- P( Neither of two cards had a heart= 1-

=

Second way:

Probability that first card drawn is a heart and the second one is not a heart= ×

=

Probability that the first card drawn is not a heart and the second one is a heart= ×

=

Probability that both cards drawn are hearts= ×

=

Adding all these probabilities, we have the probability that at least one of the card drawn was heart=

see below

Step-by-step explanation:

Part A

the probability that a randomly chosen flight arrives on time = number of flights that arrive on time/ total number of flights

Part B

The same as part A but applied for each carrier and then comparing who has the closest number to 1

Part C

total number of flights that arrives on time in PHL/ total number of flights that are on time for all airports

Part D

look for the carrier Hawaiian Airlines (HA) first and then number of flights that arrives on time for HA/ total number of flights HA has

Part E

look for OO and WN in table

add up all flights made ( all airports) for OO and WN

add up all flights on time for OO and WN

divide flights on time by all flights made

Hope this will help you. :)