Three different coins are tossed together. Find the probability of getting:

A) Exactly two heads

B) At least two heads

C) At least two tails

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\frac{3}{8}, \frac{1}{2}, \frac{1}{2}

\frac{1}{2}, \frac{1}{2}, \frac{1}{2}

\frac{4}{5}, \frac{1}{2}, \frac{2}{3}

None of the above.

answer is A.

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Detailed Solution

${"mathml":"<math class="image_resized" style="width:220px;height:36px"><span style="font-family:$ Concept- Simply said, the probability is a ratio that can be expressed as the
=
Compile a list of all the cases. Either the head or the tail can appear on each coin. This is two in number. Consider how we can put this knowledge to use.
According to the scenario, there are a total of 8 different scenarios that could occur: HHH, THH, HTH, HHT, TTH, HHT, HTT, and TTT.
A)    In the first instance, our side has exactly two heads. This suggests that there are a total of three favorable cases: THH, HTH, and HHT. Consequently, the likelihood of receiving exactly two heads is:
         ${"mathml":"<math class="image_resized" style="width:222px;height:88px"><span style="-aw-import:ignore"><span style="font-family:$ B)    At least two heads are in our favor in the second situation. What does it mean to have at least two heads? It implies that there may be more than two heads. As a result, there are four favorable cases: THH, HTH, HHT, and HHH. Consequently, the likelihood of receiving at least two heads is
         ${"mathml":"<math class="image_resized" style="width:222px;height:140px"><span style="-aw-import:ignore"><span style="font-family:$ C)    We have at least two tails in the third scenario. What does it mean to have at least two tails? Therefore, there may be more than two tails. Thus, there are four favorable instances in total: TTH, THT, HTT, and TTT. In light of this, the likelihood of at least two tails is
${"mathml":"<math class="image_resized" style="width:222px;height:140px"><span style="font-family:$       Hence, the correct answer is option 1.

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