Question

1st coin 2nd coin 3rd coin outcomes
h
h
h - - - (h,h,h)
t - - - (h,h,t)
t
h - - - (h,t,h)
t - - - (h,t,t)
t
h
h - - - (t,h,h)
t - - - (t,h,t)
t
h - - - (t,t,h)
t - - - (t,t,t)
what is the probability of getting 2 heads up and 1 tails up when flipping three coins?
○ \\(\frac{1}{6}\\)
○ \\(\frac{1}{4}\\)
○ \\(\frac{3}{8}\\)
○ \\(\frac{2}{3}\\)

Explanation:

Step1: Count total outcomes

From the tree, total outcomes: \(2\times2\times2 = 8\) (or count the 8 listed: (H,H,H), (H,H,T), (H,T,H), (H,T,T), (T,H,H), (T,H,T), (T,T,H), (T,T,T)).

Step2: Identify favorable outcomes

Favorable (2 heads, 1 tail): (H,H,T), (H,T,H), (T,H,H). So 3 outcomes.

Step3: Calculate probability

Probability = \(\frac{\text{favorable}}{\text{total}}=\frac{3}{8}\).

Answer:

\(\frac{3}{8}\) (corresponding to the option with \(\frac{3}{8}\))