Question

A fair coin is tossed three times. What is P(tossing at least two tails)?

A: one eighth
B: one fourth
C: three eighths
D: one half

Answer 1

one eighth

Step by step explanation:

Let us mark H for Heads and T for Tails.

The coin is flipped three times; the total

number of outcomes = 2 * 2 * 2 = 8 .

Sample Space (| Omega|)=\ (H, H, H), (H, H, T) ,(H,T,

H ),(H,T,T),(T,H,H),(T,H,T),(T,T,H),(T,T,T)\

= 8

Let X be the probability of getting all tails: X

= \{(T, T, T)\}

=> |X| = 1

P(X) = IXI/IQI = 1/8.

Thus, the probability of flipping a coin three times and getting 3 tails is 1/8.

Answer 2

D: one half

Explanation:

You want the probability of tossing at least two tails when a fair coin is tossed 3 times.

Outcomes

The outcomes from the tosses will be one of ...

TTT, TTH, THT, THH, HTT, HTH, HHT, HHH

Of the 8 possible outcomes, the 4 that are highlighted have at least 2 tails.

D: The probability of tossing at least 2 tails is 4/8 = 1/2.

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