Question

What is the probability of getting exactly two heads, when three coins tossed simultaneously?

Answer 1

Hint: For the above question, we will first write all the possible outcomes when three coins tossed simultaneously. Then we will count the number of favorable outcomes out of all the possible outcomes and we know that probability \[=\dfrac{\text{Number }\ \text{of }\ \text{favorable }\ \text{outcomes}}{\text{Number}\ \text{of}\ \text{all}\ \text{possible}\ \text{outcomes}}\].

Complete step-by-step solution -
We have been given three coins tossed simultaneously. Now we will have to write the sample space of the above experiment. The sample of an experiment or random trial is the set of all possible outcomes.
Also, we know that a coin has two sides one is head (H) and the one is tail (T). So, the number of sample space if we tossed three coins simultaneously are as follows:
Sample space = possible outcomes \[=\left\{ HHH, HHT, HTH, HTT, TTT, TTH, THT, THH \right\}\].
So total possible outcomes = 8.
We have been asked the probability of getting exactly two heads.
So, favorable outcomes \[=\left\{ HHT,HTH,THH \right\}\].
Number of favorable outcomes = 3.
We know that probability \[=\dfrac{\text{Number }\ \text{of }\ \text{favorable }\ \text{outcomes}}{\text{Number}\ \text{of}\ \text{all}\ \text{possible}\ \text{outcomes}}\].
Probability of getting two heads \[=\dfrac{3}{8}\].
Therefore, the probability of getting exactly 2 heads when three coins tossed simultaneously equals to \[\dfrac{3}{8}\].

Note: Be careful while writing the sample space or total possible outcomes as there is a chance of missing any one of the outcomes.