Question

Question 1

Question
The figure presents a histogram with 6 bars of data. The horizontal axis is labeled, Number of Successes, and the numbers 0 through 5, in increments of 1, are indicated. The vertical axis is labeled, Relative Frequency, and the numbers 0 through 0.45, in increments of 0.05, are indicated. The data represented in the histogram are as follows. Note that all values are approximate. Bar 1. Number of successes, 0; Relative frequency, 0.33. Bar 2. Number of successes, 1; Relative frequency, 0.39. Bar 3. Number of successes, 2; Relative frequency, 0.19. Bar 4. Number of successes, 3; Relative frequency, 0.05. Bar 5. Number of successes, 4; Relative frequency, 0.02. Bar 6. Number of successes, 5; Relative frequency, 0.02.
A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram.

Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?

Answer 1

The probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed is approximately 0.72.

Based on the results of the simulation, the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed can be estimated from the relative frequency histogram provided.

To find the probability, we need to sum the relative frequencies for the bars representing 2, 3, 4, and 5 successes (i.e., 2, 3, 4, or 5 thumbtacks landing point up) and then subtract this sum from 1, since the sum of all probabilities must equal 1.

From the given histogram, the relative frequencies for 2, 3, 4, and 5 successes are 0.19, 0.05, 0.02, and 0.02, respectively. Summing these relative frequencies, we get:

[0.19 + 0.05 + 0.02 + 0.02 = 0.28]

Subtracting this sum from 1, we find:

[1 - 0.28 = 0.72]

Therefore, the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed is approximately 0.72, which is the closest to the estimated probability based on the simulation results.

Complete question:

A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram.

Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?

A 0.09

B 0.19

C 0.28

D 0.72

E 0.91