A trick deck of cards is printed with the hearts and diamonds black, and the spades and clubs red. A card is chosen at random from this deck (after it is shuffled). Find the probability that it is either a red card or the queen of hearts. That it is either a red face card or a club. That it is either a red ace or a diamond.

The probability of any event is determined by dividing the number of favorable outcomes of a particular even to the total number of outcomes. Using this techniques probability of any event can be determined.

In a deck of card, there are 52 cards of 4 suits namely spade, club, diamond and heart, out of which spade and club are black and diamond and heart are red.

There are 13 cards of each suit and 26 cards of each color.

In the tricked deck, there are 52 cards of 4 suits namely spade, club, diamond and heart, out of which spade and club are red and diamond and heart are black.

There are 13 cards of each suit and 26 cards of each color.

In this deck of card, there is 1 queen of hearts (which is no red) and 26 red cards, this implies that total number of possibilities for a card to be a queen of heart or red is as follows,

1+26=27

This implies that the number of outcomes favorable are 27 and total number of outcomes are 52.

Write the expression for the probability.

P = number of outcomes favorable to E/total number of outcomes ...(i) Substitute the values in the above expression.

P = 27/52

In a deck of card, there are 13 club cards (which are red) and 6 red face cards out of which 3 are of clubs, this implies that total number of possibilities for a card to be a red face card or a club is 13 + 6 - 3 = 16.

This implies that the number of outcomes favorable are 16 and total number of outcomes are 52.

Substitute the values in the equation (i) to find the probability chosen card either a red face card or a club.

P = 16/52

= 4/13

In this deck of card, there are 2 red aces and 13 diamond cards, this implies that total number of possibilities for a card to be either a red ace or a diamond is 2 + 13 = 15

This implies that the number of outcomes favorable are 15 and total number of outcomes are 52.

Substitute the values in the equation (i) to find the probability the chosen card is either a red ace or a diamond.

P = 15/52

Thus, the probability that the drawn card is either a red card or the queen of hearts is 27/52, the probability chosen card either a red face card or a club is 4/13, and the probability the chosen card is either a red ace or a diamond is 15/52.