Question

carlos has 3 coins. one side of each coin is heads, and the other side is tails. the sample space for tossing all 3 coins is shown below.

first coin	second coin	third coin	end result
heads	heads	tails	hht
		heads	hth
	tails	tails	htt
		heads	thh
tails	heads	tails	tht
		heads	tth
	tails	tails	ttt

when carlos tosses all 3 coins, what is the theoretical probability he will toss exactly 2 heads and one tail?

the probability of tossing exactly 2 heads and 1 tails is

Explanation:

Step1: Count total outcomes

From the table, total number of possible outcomes (end results) when tossing 3 coins is 8 (since there are 8 rows in the table: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).

Step2: Count favorable outcomes

Now, we need to find the number of outcomes with exactly 2 heads and 1 tail. Let's list them: HHT (2 heads, 1 tail), HTH (2 heads, 1 tail), THH (2 heads, 1 tail). So there are 3 favorable outcomes.

Step3: Calculate probability

Probability is given by the formula $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Substituting the values, we get $\frac{3}{8}$.

Answer:

$\frac{3}{8}$