Question
In: Statistics and Probability
Problem 3 (a) There are 3 male and 3 female students sitting in a row, and...
Problem 3
(a) There are 3 male and 3 female students sitting in a row, and they chose their seats randomly.
What is the probably of the event "No two males sit together and no two females sit together"?
(Hint: The gender of the seated students can only be FMFMFM or MFMFMF.)
(b) Compute the probability of randomly drawing ve cards from a deck, and getting two Aces.
(Hint: A deck has 52 cards, and 4 of them are Aces.)
Solutions
Expert Solution
(a)
If there are 3 males and 3 females and six chairs then the total number of combination,
The combinations are
{FFFMMM FFMFMM FFMMFM FFMMMF FMFFMM FMFMFM FMFMMF FMMFFM FMMFMF FMMMFF MFFFMM MFFMFM MFFMMF MFMFFM MFMFMF MFMMFF MMFFFM MMFFMF MMFMFF MMMFFF}
Number of combination where no two males sit together and no two females sit together = 2
The combinations are = {MFMFMF, FMFMFM}
The probability that No two males sit together and no two females sit together ,
(b)
Probablity of getting ace in first draw = 4/52
Probability of getting ace in second draw = 3/51
Therefore the probability of getting ace in both draws ,
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