Question

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: Determine the total number of outcomes

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

Step2: Solve part (a)

The events with at least two tails are \( \{TTT, TTH, THT, HTT\} \), so \( n(A)=4 \)
The probability \( P(A)=\frac{n(A)}{n(S)}=\frac{4}{8}=0.5 \)

Step3: Solve part (b)

The events with exactly one head are \( \{TTH, THT, HTT\} \), so \( n(B) = 3 \)
The probability \( P(B)=\frac{n(B)}{n(S)}=\frac{3}{8}=0.375 \)

Step4: Solve part (c)

The event with no head is \( \{TTT\} \), so \( n(C)=1 \)
The probability \( P(C)=\frac{n(C)}{n(S)}=\frac{1}{8}=0.125 \)

Answer:

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