Answer to Question #339827 in Statistics and Probability for Rookie

Question #339827

Pls Include solution:)

 A coin tossed thrice. Find: 

 a. The probability of getting exactly 3 heads. 

 b. The probability of getting exactly 2 tails.

 c. The probability of getting atmost 1 head. 

 d. The probability of getting atleast 1 tail.


1
Expert's answer
2022-05-12T09:03:36-0400

The sample space of a fair coin flip is {H,T}.\{H, T\}. The sample space of a sequence of three fair coin flips is all 23=82^3=8 possible sequences of outcomes:


{HHH,HHT,HTH,HTT,\{ HHH, HHT, HT H, HT T,THH,THT,TTH,TTT}T HH, T HT, T T H, T T T\}


a.

Exactly 3 heads: HHHHHH


P(exactly 3 heads)=18P(exactly\ 3\ heads)=\dfrac{1}{8}

b.

Exactly 2 tails: HTT,THT,TTHHTT, THT, TTH


P(exactly 2 tails)=38P(exactly\ 2\ tails )=\dfrac{3}{8}


c.

At most 1head: HTT,THT,TTH,TTTHTT, THT, TTH, TTT


P(at most 1 head)=48=12P(at\ most\ 1\ head)=\dfrac{4}{8}=\dfrac{1}{2}

d.

At least 1 tail:HHT,HTH,HTT,THH,THT,TTH,TTTHHT, HT H, HT T, T HH, T HT, T T H, T T T


P(at least 1 tail)=78P(at\ least\ 1\ tail)=\dfrac{7}{8}

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