Find the probability of getting 2 or 3 tails whena coin is tossed four times.

Answer

To find the probability of getting 2 or 3 tails when a coin is tossed four times, we can follow these steps:

### Step 1: Determine the total number of outcomes
When a coin is tossed \( n \) times, the total number of possible outcomes is given by \( 2^n \). In this case, since the coin is tossed 4 times:

\[ \text{Total outcomes} = 2^4 = 16 \]

### Step 2: Identify the favorable outcomes
We need to find the number of outcomes that result in either 2 tails or 3 tails.

#### Finding outcomes with 2 tails:
To find the number of ways to get exactly 2 tails in 4 tosses, we can use the binomial coefficient:

\[ \text{Number of ways to get 2 tails} = \binom{4}{2} \]

Calculating this:

\[ \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 \]

#### Finding outcomes with 3 tails:
Similarly, for exactly 3 tails:

\[ \text{Number of ways to get 3 tails} = \binom{4}{3} \]

Calculating this:

\[ \binom{4}{3} = \frac{4!}{3!(4-3)!} = \frac{4}{1} = 4 \]

### Step 3: Calculate the total favorable outcomes
Now, we add the number of outcomes with 2 tails and 3 tails:

\[ \text{Total favorable outcomes} = \text{Number of ways to get 2 tails} + \text{Number of ways to get 3 tails} = 6 + 4 = 10 \]

### Step 4: Calculate the probability
The probability \( P \) of getting 2 or 3 tails is given by the ratio of favorable outcomes to total outcomes:

\[ P(\text{2 or 3 tails}) = \frac{\text{Total favorable outcomes}}{\text{Total outcomes}} = \frac{10}{16} \]

Simplifying this fraction:

\[ P(\text{2 or 3 tails}) = \frac{5}{8} \]

### Final Answer
The probability of getting 2 or 3 tails when a coin is tossed four times is \( \frac{5}{8} \).

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