Can you please answer the following MCQ showing any equations and steps? 1- In a
ID: 3131847 • Letter: C
Question
Can you please answer the following MCQ showing any equations and steps?
1- In a game of cards the first player is dealt 5 cards from a full deck of 52 cards. What is the probability the player is dealt “four of a kind” correct to 2 significant
figures?
{Aside: A full deck has 4 different suits: Hearts, Clubs, Diamonds and Spades.
Within each suit are 13 different denominations of card: the numbers 2 to 10 and Jack, Queen, King, Ace. “Four of a kind” requires four cards of the same denomination in the 5 cards dealt}.
(a) 6.0 x 10-7
(b) 5.0 x 10-8
(c) 2.4 x 10-4
(d) None of the above.
2- Which of the following statements is true?
(a) The volume of beer sold in the UCD student bar on a given night is a continuous random variable; the number of pints sold is a discrete random variable.
(b) The volume of beer sold in the UCD student bar on a given night is a discrete random variable; the number of pints sold is also a discrete random variable.
(c) The volume of beer sold in the UCD student bar on a given night is a continuous random variable; the number of pints sold is also a continuous random variable.
(d) The volume of beer sold and the number of pints sold are not random variables.
3- Consider the following discrete probability distribution, where one of the probabilities is missing:
Y: 0 4 8 12 20
P(Y): 0.4 0.3 K 0.1 0.04
What is the missing probability K ?
(a) 0.06
(b) -0.84
(c) 0.84
(d) None of the above.
0.1 0.04
7. Consider the following discrete probability distribution:
M: 0.1 0.2 0.7 0.8 1.0
P(M): 0.5 0.15 0.1 0.2 0.05
What is the variance of M, correct to three decimal places ?
(a) 0.330
(b) 0.108
(c) 0.026
(d) None of the above
Explanation / Answer
1.
There are 13 ways to get a 4 of a kind. Then, there are 48 ways to get the 5th card. Hence, a total of
13*48 = 624 ways to do the job.
There are 52C5 = 2598960 ways to get any 5 cards.
Hence,
P(four of a kind) = 624/2598960 = 0.000240096 = 2.4*10^-4 [ANSWER, C]
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