Question Type 4: Working with expected occurrences and probabilities Bootcamps

The probability of rain on any given day is $0.2$. If it rained on 14 days, how many days were observed?

In a survey of 300 people, 180 answer “yes” on average. What is the probability $p$ of a “yes” response?

A spinner lands on blue with probability $\tfrac{1}{5}$. If blue appears 40 times, how many spins are there in total?

In a game, the probability of success is $0.4$. If 80 successes are expected, how many plays are needed?

A loaded die has probability $0.2$ of rolling a six. After 200 rolls, what is the expected number of sixes?

The probability that a customer makes a purchase is $0.08$. If a store records 24 purchases, estimate the number of visitors.

Fruit flies have a probability of $0.15$ of carrying a certain gene. If 45 carriers are observed on average, how many flies were tested?

A biased coin lands heads with unknown probability $p$. In 1000 tosses, you observe on average 520 heads. Find $p$.

A factory’s defect rate is $0.03$. If 150 defectives are expected, find the total number of products inspected.

A rare disease occurs with probability $0.001$ in a population. If 50 cases are expected, how many individuals are in the population?

Events $A$ and $B$ are independent with probabilities $P(A)=0.3$ and $P(B)=0.5$. In 1000 trials, what is the expected number of trials where both $A$ and $B$ occur?

Events $A$ and $B$ are independent with $P(A)=0.2$ and $P(B)=0.4$. In 500 trials, what is the expected number of trials where at least one of $A$ or $B$ occurs?