Two coins are tossed. a. Find the probability that both are heads

pro4ph5e4q2

pro4ph5e4q2

Answered question

2021-11-15

Two coins are tossed.
a. Find the probability that both are heads
b. Find the probability that one is heads and one is tails.
c. Find the probability that both are tails.
d. Which is more likely: that the two coins match or that they don’t match? Why?

Answer & Explanation

Alfonso Miller

Alfonso Miller

Beginner2021-11-16Added 20 answers

Step 1
Let us denote H=head and T=tail
When two coins are tossed then the possible outcomes are {HH, HT, TH, TT}
So there are 4 outcomes
Step 2
a) There is only one outcome for both heads. {HH}
the probability that both are heads =n(both heads)n(total outcomes)=14=0.25
Answer(a): 0.25
Step 3
a) There are two outcomes for one is heads and one is tails. {HT, TH}
the probability that one is heads and one is tails =n(one is heads and one is tails)n(total outcomes)=24=0.5
Answer(b): 0.5
Step 4
c) There is only one outcome for both tails. {TT}
the probability that both are tails =n(both tails)n(total outcomes)=14=0.25
Answer(c): 0.25
Step 5
d) Probability that two coins match {HH,TT} is =0.25+0.25=0.5
The probability that they do not match {HT,TH} is =0.5
So both events are equally likely because both have the same probability.

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