Question

q30.) a coin is tossed three times. what is the probability the coin will land on the same outcome all three tosses? 1st toss 2nd toss 3rd toss outcomes

Explanation:

Step1: Find total number of outcomes

Each coin - toss has 2 possible outcomes. Since the coin is tossed 3 times, by the multiplication principle, the total number of outcomes is \(2\times2\times2 = 2^{3}=8\).

Step2: Identify favorable outcomes

The favorable outcomes (landing on the same side all three times) are either all - heads (HHH) or all - tails (TTT), so there are 2 favorable outcomes.

Step3: Calculate probability

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{2}{8}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)