Arrange the given events in ascending order of their probabilities
A = target is hit 2 times in 20 shots.
B = target is hit 175 times in 200 shots.
C = target is hit 92 times in 100 shots.
D = target is hit 2 times in 5 shots.
E = target is hit 5 times in 13 shots.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, E, D, B, C
The probability of hitting the target is the number of hits divided by the number of shots. Written as decimals, the five probabilities can be compared at once.
A, 2 hits in 20 shots: \(\frac{2}{20}=0.1\)
B, 175 hits in 200 shots: \(\frac{175}{200}=0.875\)
C, 92 hits in 100 shots: \(\frac{92}{100}=0.92\)
D, 2 hits in 5 shots: \(\frac{2}{5}=0.4\)
E, 5 hits in 13 shots: \(\frac{5}{13}\approx0.385\)
From the smallest to the largest: 0.1 (A), 0.385 (E), 0.4 (D), 0.875 (B), 0.92 (C). E and D are the close pair: \(\frac{5}{13}\) is a little less than \(\frac{5}{12.5}=\frac{2}{5}\), so E comes before D.