Problem
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 300 trials, the touch therapists were correct 144 times. Complete parts (a) through (d). a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? (Type an integer or a decimal. Do not round.)
Solution
Step 1 ：Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
Step 2 ：The coin toss is a random event with two equally likely outcomes. Therefore, if the touch therapists were making random guesses, we would expect them to be correct about half of the time.
Step 3 ：\(\text{expected\_proportion} = 0.5\)
Step 4 ：\(\boxed{\text{The expected proportion of correct responses if the touch therapists made random guesses is } 0.5}\)
