determine the following if 3 fair coins are tossed with possible outcomes of heads, h, and tails, t. a)…

determine the following if 3 fair coins are tossed with possible outcomes of heads, h, and tails, t. a) write a sample space with equally likely outcomes. b) find the probability of tossing at least 1 head. a) what is the sample space when tossing 3 coins? (use a comma to separate answers as needed.)

determine the following if 3 fair coins are tossed with possible outcomes of heads, h, and tails, t. a) write a sample space with equally likely outcomes. b) find the probability of tossing at least 1 head. a) what is the sample space when tossing 3 coins? (use a comma to separate answers as needed.)

Answer

Explanation:

Step1: List all possible outcomes

Each coin has 2 possible outcomes. For 3 - coin tosses, we use the multiplication principle. The sample - space is found by considering all combinations. {hhh, hht, hth, thh, htt, tht, tth, ttt}

Step2: Calculate the probability of the complement event

The complement of the event “at least 1 head” is “no heads” (i.e., all tails). The total number of outcomes in the sample - space $n(S)=8$ (from step 1). The number of outcomes with no heads $n(E_{complement}) = 1$ (the outcome ttt). The probability of the complement event $P(E_{complement})=\frac{n(E_{complement})}{n(S)}=\frac{1}{8}$.

Step3: Calculate the probability of the original event

We know that $P(E)=1 - P(E_{complement})$. So $P(\text{at least 1 head})=1-\frac{1}{8}=\frac{7}{8}$.

Answer:

a) hhh, hht, hth, thh, htt, tht, tth, ttt b) $\frac{7}{8}$