Question

19. Charlotte has a success rate of about 20%
for making baskets in attempts during
basketball games. She wants to determine
the probability that she will have to make at
least 5 attempts during a game in order to
make a basket. She designed a simulation
where she spun a spinner that was divided
into 5 equal sections, one of which was
colored red. She counted how many times
she had to spin the spinner in each trial
before it landed on red. The results of her
20 trials are shown below.
5, 2, 7, 2, 3, 4, 10, 6,4,6,
3, 6, 6, 4, 8,5,7,7,1,5
According to this simulation, what is the
probability that Charlotte will have to
make at least 5 attempts in order to make
a basket?

Answer 1

Answer:

$P(x \ge 5) = 0.60$

Step-by-step explanation:

Given

$S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}$

$n(S) = 20$

Required

$P(x \ge 5)$

First, we count the number of trials that are at least 5

$x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}$

So, we have:

$n(x \ge 5) = 12$

So, we have:

$P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}$

This gives

$P(x \ge 5) = \frac{12}{20}$

$P(x \ge 5) = 0.60$