My Courses > CRN 40938 Chapter 4 HW - Discrete Random Variable Curren \( { }^{+} \)A! Category: Homework An unfair coin is flipped 10 times. The probability of getting heads in one coin toss is \( p=0,65 \). Each flip is independent. a) Let \( X= \) the number of heads in 10 flips of the unfair coin. What values does \( X \) takes on? Enter your answer \( \square \) (Give your answer as a list of numbers separated by commas.) b) What is the probability of failure (getting tails)? \( q= \) \( \square \) Enter your answer \( \sqrt{x} \) (Give the exact value as a decimal number.) c) You want to find the probability of getting heads more than three times. Which of the following states the probability question mathematically? A \( P(x<3) \) B \( P(x>3) \) C \( P(x \leq 3) \) D \( P(x \geq 3) \) Submit answer Attempts: 0/10
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The values that \( X \) can take on represent the possible counts of heads in 10 flips, ranging from 0 to 10. Thus, \( X \) can take on the values \( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \). The probability of getting tails is simply the complement of getting heads. Since \( p = 0.65 \) for heads, the probability of tails, or \( q \), is calculated as \( q = 1 - p = 1 - 0.65 = 0.35 \). So, \( q = 0.35 \). For the probability of getting heads more than three times, the correct mathematical representation is \( P(x > 3) \), as it specifically asks for scenarios where the count of heads exceeds three. So the answer is B.
