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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orchestra answered 1 year ago

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