🎲 probability

1. **Problem statement:** We have a city where births occur at a rate of one birth every 12 minutes, and the time between births follows an exponential distribution. We need to fin

1. **State the problem:** James wants to remove balls from a bag without looking, to guarantee he has at least 4 balls of different colors (red, blue, black, yellow). 2. **Given:**

1. **Stating the problem:** Given probabilities about piers and destinations on Coconut Island, we find various probabilities for one or two travelers, and then calculate the numbe

1. Problem: Find the probability of drawing a card with an odd number or a prime number from an ordinary deck. 2. Step 1: Determine the total number of cards in the deck. An ordina

1. **State the problem:** We want to find the sample space for the gender of five children in a family. 2. **Understanding sample space:** Each child can be either a boy (B) or a g

1. **State the problem:** We need to find the probability that an animal chosen at random from tank B is either a lobster or a ray. 2. **Identify the quantities:** From the bar cha

1. **Problem statement:** We have a population where 8% actually have COVID-19. The test has a true positive rate of 92% and a false positive rate of 6%. We want to find: 1. Probab

1. Problem: A spinning wheel has 3 green sectors, 1 blue sector, and 1 red sector, totaling 5 sectors. 2. Calculate the probability of each event as the ratio of favorable outcomes

1. The quiz has 10 questions, each with 6 possible answers, and answers are guessed randomly. 2. Passing requires at least 70% correct, so minimum correct answers to pass is $\lcei

1. **State the problem:** We have a spinner divided into 3 equal sections labeled 1, 2, and 3, spinning fairly. 2. **Part (a):** Find the probability of spinning a 2.

1. The problem states that the probability of the spinner landing on a striped section is $\frac{7}{10}$. We want to find the expected number of times it lands on a striped section

1. Problem: Determine which pairs of events are independent when drawing a single card from a standard 52-card deck. 2. Recall that two events A and B are independent if $$P(A \cap

1. Problem: Todd's locker combination has two numbers, each can be from 1 to 6. 2. We want the probability that Todd guesses the first number correctly and the second number incorr

1. The problem is to find the probability of getting between 2 and 5 heads inclusive in 9 tosses of a fair coin. This means finding $P(2 \leq X \leq 5)$ where $X$ is the number of

1. **Problem Statement:** Find the probability of getting between 2 and 5 heads inclusive in 9 tosses of a fair coin.

1. **Problem Statement:** James rolls a fair six-sided die and draws one card from 17 cards numbered 1 to 17. We are asked to solve four parts related to this experiment. 2. **(a)

1. **State the problem:** We want to find two probabilities based on the Venn diagram data of 45 dancers who like tango (T), hip-hop (H), or quick-step (Q). 2. **Identify the numbe

1. Nyatakan masalah: Kita ingin mengira kebarangkalian memilih seorang lelaki dan seorang perempuan dari keluarga Aziz dan Deeva yang terdiri daripada jumlah lelaki dan perempuan y

1. Problem statement: We have two families with the following members:

1. **Problem statement:** We toss a fair coin 3 times. (1) Find the probability of exactly 2 heads.

1. **State the problem:** We toss a fair coin 3 times and want to find (1) the probability of exactly 2 heads, (2) the probability of more than 1 tail, and (3) the probability of a