Question

An unbiased coin is tossed 4 times. The probability of getting exactly 2 heads and 2 tails in any order is ........... (decimal digits up to 2 places)

Hint:

For problems with a fixed number of heads and tails, use combinations to calculate the number of favorable outcomes.

Answer 1

Correct Answer: 0.36

Step 1: Find the total number of possible outcomes.
For 4 tosses of an unbiased coin, there are \( 2^4 = 16 \) possible outcomes.

Step 2: Use combinations to find the number of favorable outcomes.
We need to find the number of ways to get exactly 2 heads and 2 tails in 4 tosses. This is a combination problem, where we choose 2 positions for heads out of 4 tosses: \[ \text{Number of favorable outcomes} = \binom{4}{2} = \frac{4!}{2!(4-2)!} = 6. \]

Step 3: Calculate the probability.
The probability of getting exactly 2 heads and 2 tails is: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{16} = 0.375. \]

Step 4: Conclusion.
The probability of getting exactly 2 heads and 2 tails in any order is 0.375.