Question

wednesday, september 24th, 2025
bellwork non - iphones put away

1. describe what conditional probability is in general terms. (see mon lesson)
2. what is the formula for conditional probability? (see mon lesson)
3. a basketball player typically makes 80% of their free throw attempts.

calculate the following probabilities:
a. p(make 3 in a row)
b. p(make 10 in a row)
c. p(miss 2 in a row)
d. p(miss 4 in a row)

Explanation:

Step1: Identify the probabilities of making and missing

The probability of making a free - throw $p = 0.8$, and the probability of missing a free - throw $q=1 - p=0.2$. Since free - throw attempts are independent events, for independent events $A$ and $B$, $P(A\cap B)=P(A)\times P(B)$.

Step2: Calculate $P(\text{make }3\text{ in a row})$

Using the multiplication rule for independent events, $P(\text{make }3\text{ in a row})=0.8\times0.8\times0.8 = 0.8^{3}=0.512$.

Step3: Calculate $P(\text{make }10\text{ in a row})$

$P(\text{make }10\text{ in a row})=0.8^{10}\approx0.1074$.

Step4: Calculate $P(\text{miss }2\text{ in a row})$

$P(\text{miss }2\text{ in a row})=0.2\times0.2 = 0.2^{2}=0.04$.

Step5: Calculate $P(\text{miss }4\text{ in a row})$

$P(\text{miss }4\text{ in a row})=0.2\times0.2\times0.2\times0.2=0.2^{4}=0.0016$.

Answer:

for 1:
Conditional probability is the probability of an event occurring given that another event has already occurred. It measures the likelihood of an event $A$ happening under the condition that event $B$ has taken place, and it reflects how the knowledge of one event affects the probability of another.