Question

a school conducts a recipe contest in which 1 student gets first place, 1 student gets second place, 1 student gets third place, and 10 students tie for fourth place. fifty students enter the contest. if x represents the distribution of prizes, which graph represents the probability distribution for a randomly selected student? two probability distribution graphs are shown, with the first having categories no prize, 1st, 2nd, 3rd, 4th and corresponding bars, and the second partially visible

Explanation:

Step1: Calculate number of no - prize students

Total students = 50. Number of students with prizes: 1 (1st) + 1 (2nd) + 1 (3rd) + 10 (4th) = 13. So number of students with no prize = 50 - 13 = 37.

Step2: Calculate probabilities

• Probability of 1st place: $P(1st)=\frac{1}{50} = 0.02$
• Probability of 2nd place: $P(2nd)=\frac{1}{50}=0.02$
• Probability of 3rd place: $P(3rd)=\frac{1}{50} = 0.02$
• Probability of 4th place: $P(4th)=\frac{10}{50}=0.2$
• Probability of no prize: $P(\text{no prize})=\frac{37}{50} = 0.74$ (close to 0.7 as in the first graph)

Now, check the graph: The first graph has "No Prize" with a high probability (around 0.7 - 0.74), "1st", "2nd", "3rd" with very low probabilities (around 0.02), and "4th" with probability around 0.2. The second graph's axis and labels seem inconsistent (e.g., y - axis has 10, 25, 40 which are not probabilities between 0 and 1). So the first graph (the one with "No Prize", "1st", "2nd", "3rd", "4th" on x - axis and probability on y - axis) is correct.

Answer:

The top graph (the first "Probability Distribution" graph with x - axis labels "No Prize", "1st", "2nd", "3rd", "4th" and y - axis for probability)