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Probability, SM-Bank 008 MC

A standard deck of 52 cards is made up of four suits - Hearts, Diamonds, Clubs and Spades.

Each suit contains 13 cards that include an Ace, King, Queen and Jack, together with numbered cards from 2 to 10.

Lara has a standard deck of cards and without looking, picks a number 7 and returns it to the deck.

She repeats this three times and draws a number 7 each time.

If she draws a 4th card without looking, which of the following is true?
 

  1. She is certain to draw a number 7.
  2. She is more likely to draw a number 7 than a Spade.
  3. She is less likely to draw a number 7 than a Queen.
  4. She is more likely to draw a Heart than a number 7.
Show Answers Only

\(D\)

Show Worked Solution

\(\text{There are 13 hearts in the deck}\)

\(\text{There are 13 spades in the deck}\)

\(\text{There are 4 7’s in the deck}\)

\(\text{There are 4 queens in the deck}\)
 

\(\text{Consider Option D}\ \rightarrow\ \text{There are more hearts than 7’s}\)

\(\therefore\ \text{She is more likely to draw a heart than a 7}\)

 
\(\Rightarrow D\)