Answer to Question #339827 in Statistics and Probability for Rookie

Question

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.

Answer 1

The sample space of a fair coin flip is $\{H, T\}.$ The sample space of a sequence of three fair coin flips is all $2^3=8$ possible sequences of outcomes:

$$\{ HHH, HHT, HT H, HT T,$$ $$T HH, T HT, T T H, T T T\}$$

a.

Exactly 3 heads: $HHH$

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

b.

Exactly 2 tails: $HTT, THT, TTH$

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

c.

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

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

d.

At least 1 tail:$HHT, HT H, HT T, T HH, T HT, T T H, T T T$

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