Three unbiased coins are tossed. What is the probability of getting atmost two heads?

Three unbiased coins are tossed. What is the probability of getting atmost two heads? Correct Answer <span class="math-tex">\(\frac{7}{8}\)</span>

The correct answer is ​​​7/8.​

Key Points

• Given, three unbiased coins are tossed together.
• The possible cases or outcomes which will arise are given by (H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T).
• Here H represents head occurring and T represents tail occurring.
• As we know that the general formula for probability is the Probability of occurrence of an event=Total number of favorable outcomes/Total number of possible outcomes.
• Getting at most Two heads means 0 to 2 but not more than 2
• Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
• Let E = event of getting at most two heads
• Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}
• So, P(E)=n(E)n(S)=7/8. Hence, Option 2 is correct.

Additional Information

• Probability
  • It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
  • The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.