Medium - Quiz 1

Move beyond basic counts into conditional probability, two-way tables, overlapping events, and the complement strategy for 'at least one' problems.

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Question 1

A gym surveyed 200 members about their preferred workout. The results are shown below. \[\begin{array}{|c|c|c|c|c|} \hline & \textbf{Gym} & \textbf{Running} & \textbf{Yoga} & \textbf{Total} \\ \hline \textbf{Under 30} & 40 & 35 & 25 & 100 \\ \textbf{30 and over} & 20 & 30 & 50 & 100 \\ \hline \textbf{Total} & 60 & 65 & 75 & 200 \\ \hline \end{array}\] If a member under 30 is selected at random, what is the probability that the member prefers yoga?

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A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn at random without replacement. What is the probability that at least one marble is red?

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One card is drawn at random from a standard 52-card deck. What is the probability that the card is either a face card (Jack, Queen, or King) or a heart?

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In a certain city, the probability of rain on any given day in April is 0.4. Assume weather on different days is independent. If a student randomly selects 2 days in April for outdoor events, what is the probability that it rains on both days?

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A company surveyed 150 employees about their commute. Some values in the table are missing. \[\begin{array}{|c|c|c|c|c|} \hline & \textbf{Car} & \textbf{Transit} & \textbf{Bike} & \textbf{Total} \\ \hline \textbf{Full-time} & ? & 30 & 10 & 90 \\ \textbf{Part-time} & 25 & ? & 15 & 60 \\ \hline \textbf{Total} & 75 & 50 & 25 & 150 \\ \hline \end{array}\] What is the probability that a randomly selected employee is part-time and uses public transit?

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