Question

section 5.3 homework score: 8/13 answered: 8/13 question 9 you toss a fair coin 4 times. what is the probability that (round to 4 decimal places) a) you get all tails? enter an integer or decimal number, accurate to at least 4 decimal places (more...) b) you get at least one head?

Explanation:

Step1: Calculate total number of outcomes

Each coin - toss has 2 possible outcomes. When tossing a coin 4 times, by the multiplication principle, the total number of possible outcomes is $2\times2\times2\times2 = 2^4=16$.

Step2: Calculate probability of all - tails

The event of getting all tails is 1 specific outcome. The probability $P(A)$ of an event $A$ is given by $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of getting all tails is $\frac{1}{16}=0.0625$.

Step3: Calculate probability of at least one head

The complement of the event “getting at least one head” is the event “getting all tails”. Let $B$ be the event of getting at least one head and $A$ be the event of getting all tails. Then $P(B)=1 - P(A)$. Since $P(A) = 0.0625$, then $P(B)=1 - 0.0625 = 0.9375$.

Answer:

a) 0.0625
b) 0.9375