2. Hayter text: 3.2.7 Cards are chosen randomly from a pack of cards with replacement. Calculate the probability that: (a) The first heart is obtained on the third drawing. (b) The fourth heart is obtained on the tenth drawing. (c) What is the expected number of cards drawn before the fourth heart is obtained? (d) If the first two cards drawn are spades, what is the probability that the first heart is obtained on the fifth drawing?
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The probability of drawing a heart is $p = \frac{13}{52} = \frac{1}{4}$. The probability of not drawing a heart is $1-p = \frac{3}{4}$. We want the first two draws to be non-hearts and the third draw to be a heart. The probability is $(\frac{3}{4})^2 \cdot Show more…
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Adi S.
3. Find the theoretical probability of: a. Drawing a red ace or a heart from a regular deck of cards. (4 marks) b. When guessing the birthdays of two friends, getting exactly one right, if you know the first friend was born in a leap year and the second friend wasn’t. Assume birthdays are evenly distributed throughout the year. (4 marks) c. Being dealt at least 4 hearts in a hand of 5 cards dealt from a regular deck. (5 marks) d. When selecting 3 cards from a regular deck without replacement, having the 3rd card be the second spade drawn. (5 marks)
Joanna Q.
1.3-4. Two cards are drawn successively and without replacement from an ordinary deck of playing cards. Compute the probability of drawing (a) Two hearts. (b) A heart on the first draw and a club on the second draw. (c) A heart on the first draw and an ace on the second draw. HINT: In part (c), note that a heart can be drawn by getting the ace of hearts or one of the other 12 hearts.
Steven C.
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