Question

a local charity holds a carnival to raise money. in one activity, participants make a $3 donation for a chance to spin a wheel that has 10 spaces with the values, 0, 1, 2, 5, and 10. whatever space it lands on, the participant wins that value. let x represent the value of a random spin. the distribution is given in the table. which of the following is the correct interpretation of ( p(x < 5) )? the probability of a random spin having a value of at most 5 is 0.8. the probability of a random spin having a value of at least 5 is 0.2. the probability of a random spin having a value lower than 5 is 0.8. the probability of a random spin having a value higher than 5 is 0.1.

Explanation:

The notation \(P(X < 5)\) means the probability that the random variable \(X\) (value of a spin) is less than 5. Looking at the values in the table, the values less than 5 are 0, 1, and 2. The probabilities for these values are \(0.4\), \(0.2\), and \(0.2\) respectively. Summing these probabilities (\(0.4 + 0.2+0.2=0.8\)) gives the probability that \(X\) is less than 5.

Answer:

The probability of a random spin having a value lower than 5 is 0.8.