Question

question 13
3 pts
the sample space for tossing a coin three times is:
$s = { hhh, hht, hth, thh, ttt, tth, tht, htt }$
note #1: in your answer that is to be entered in the box below, please do not omit the 0 that comes before the decimal point: that is, enter decimal values as 0.561, not.561
note #2: enter your answer without rounding it.
a) what is the probability of obtaining at least two tails?
b) what is the probability of obtaining exactly one head?
c) what is the probability of obtaining no head?

Explanation:

Step1: Calculate total number of outcomes

The sample space \( S=\{HHH, HHT, HTH, THH, TTT, TTH, THT, HTT\} \), so \( n(S) = 8 \)

Step2: Solve part (a)

At - least two tails means two or three tails.
The outcomes with at - least two tails are \( \{TTT, TTH, THT, HTT\} \), so \( n(A)=4 \)
Probability \( P(A)=\frac{n(A)}{n(S)}=\frac{4}{8}=0.5 \)

Step3: Solve part (b)

Exactly one head means two tails and one head.
The outcomes with exactly one head are \( \{TTH, THT, HTT\} \), so \( n(B) = 3 \)
Probability \( P(B)=\frac{n(B)}{n(S)}=\frac{3}{8}=0.375 \)

Step4: Solve part (c)

No head means all tails.
The outcome with no head is \( \{TTT\} \), so \( n(C)=1 \)
Probability \( P(C)=\frac{n(C)}{n(S)}=\frac{1}{8}=0.125 \)

Answer:

a) \( 0.5 \)
b) \( 0.375 \)
c) \( 0.125 \)