Question

the probability that liu yang makes a three - point shot in basketball is 10%. for practice, liu yang will regularly shoot a series of these shots until she makes one. shes curious how many shots it will typically take her to get her first successful shot.
she simulated 30 trials of three - point shots where each shot had a 0.1 probability of being made, and in each trial, she counted how many shots it took to get the first successful shot. here are her results:
use her results to estimate the probability that it takes 11 or more shots to get her first successful shot.
give your answer as either a fraction or a decimal.
$p(11$ or more shots$)\approx\square$

Explanation:

Step1: Count the total number of trials

The total number of trials \( n = 30 \).

Step2: Count the number of trials with 11 or more shots

By looking at the dot - plot, we count the number of dots for \( x = 11,12,\cdots,28 \). The number of dots for 11 or more shots \( m=1 + 3+2 + 1+1+1+1+1=11 \).

Step3: Calculate the probability

The probability \( P=\frac{m}{n} \). Substituting \( m = 11 \) and \( n = 30 \), we get \( P=\frac{11}{30}\approx0.37 \).

Answer:

\( 0.37 \) (or \(\frac{11}{30}\))