Question

11. What are the possible combination outcomes when you toss a fair coin three times? (6.25 points) H = Head, T = Tail a {HHH, TTT) Ob. (HHH, TTT, HTH, THT) c. {HHH, TTT, HTH, THT, HHT, TTH, THH) d. (HHH, TTT, HTH, THT, HHT, TTH, THH, HTT} e. None of these 12. What is the probability of you getting three heads straight for tossing a fair coin three times? (6.25 points) a. 1/2 OD. 1/4 C. 118 d. 1/16 13. What is the probability of you getting no heads at all for tossing a fair coin three times? (6.25 points) . a. 112 D. 114 C 1/8 d. 1/16

Answer 1

11) What are the possible combination outcomes when you toss a fair coin three times?

The correct answer is Option (d): $[HHH,TTT,HTH,THT,HHT,TTH,THH,HTT]$

There are 8 possible outcomes when we toss a fair coin three times.

12) What is the probability of you getting three heads straight for tossing a fair coin three times?

The correct answer is Option (c): $1/8$

The sample space for tossing a fair coin three times is,

$S=[HHH,TTT,HTH,THT,HHT,TTH,THH,HTT]$

Number of possible outcomes in sample space $n(S)=8$

Let A be the event of getting three heads.

$A=[HHH]$

Number of outcomes with three heads $n(A)=1$

We know that,

Probability = Number of favourable outcomes / Total number of outcomes

The probability of getting three heads straight for tossing a fair coin three times is,

$P[A]=n(A)/n(S)$

  $=1/8$

13) What is the probability of you getting no heads at all for tossing a fair coin three times?

The correct answer is Option (c): $1/8$

The sample space for tossing a fair coin three times is,

$S=[HHH,TTT,HTH,THT,HHT,TTH,THH,HTT]$

Number of possible outcomes in sample space $n(S)=8$

Let B be the event of getting no heads at all.

$B=[TTT]$

Number of outcomes with no heads $n(B)=1$

We know that,

Probability = Number of favourable outcomes / Total number of outcomes

The probability of getting no heads at all for tossing a fair coin three times is,

$P[B]=n(B)/n(S)$

  $=1/8$