🎲 probability

1. **State the problem:** We draw one card from a standard 52-card deck. Event $E$ is drawing a club. We want to find the probability of the complement event $E'$, which means draw

1. **State the problem:** We want to find the probability of having 7 girls in a family with 7 children, assuming each child is equally likely to be a girl or a boy. 2. **Formula u

1. **State the problem:** We need to find the probability that a card drawn from a standard deck of 52 cards is either a black card or a 5. 2. **Recall the formula for probability

1. **State the problem:** You pay 10 to play a game where two fair dice are rolled, and you receive a payout equal to the sum of the dice. The net gain is the payout minus 10. We w

1. **State the problem:** We draw one card from a standard 52-card deck. Event $E$ is drawing a jack. We want to find the probability of the complement event $E'$, which means draw

1. **State the problem:** We want to find the probability of having 2 girls in a family with 2 children, assuming each child is equally likely to be a girl or a boy. 2. **Formula a

1. **State the problem:** We need to find the probability that a card drawn from a standard deck of 52 cards is either a black card or a 3. 2. **Recall the formula for probability

1. **State the problem:** We have a box with 4 red, 2 white, and 2 green balls. Two balls are drawn one after the other without replacement. We want to find the probability that bo

1. **Problem statement:** We have a box with 5 red and 3 white balls (total 8 balls). Two balls are drawn in succession. 2. **Goal:** Find the probability that the second ball draw

1. **Problem Statement:** We have a box with 5 red and 3 white balls (total 8 balls). Two balls are drawn in succession. (A) Find the probability that the second ball is red given

1. **Problem Statement:** Find the probability that the first card drawn is red and the second card drawn is black from a standard 52-card deck. 2. **Key Information:**

1. **Problem Statement:** Find the probability that the first card drawn is red and the second card drawn is black from a standard 52-card deck. 2. **Key Information:**

1. The problem asks to find the probabilities (A) $P(M \cap S)$ and (B) $P(R)$ using the given probability tree. 2. From the tree, the first split is between $M$ and $R$ with proba

1. **State the problem:** We need to find the conditional probability $P(C|D)$, which is the probability of event $C$ occurring given that event $D$ has occurred. 2. **Recall the f

1. **State the problem:** We need to find the conditional probability $P(D|C)$, which is the probability of event $D$ occurring given that event $C$ has occurred. 2. **Formula:** T

1. The problem asks to find the probability of the intersection of events C and E, denoted as $P(C \cap E)$. 2. From the table, $P(C \cap E)$ is the probability where both C and E

1. **State the problem:** We need to find the probability of event C, denoted as $P(C)$. 2. **Understand the table:** The table shows joint probabilities of events A, B, C with D,

1. **State the problem:** We want to find the conditional probability that neither die shows a 2 given that the sum of the two dice is greater than 8. 2. **Recall the formula for c

1. **State the problem:** We need to find the probability of rolling a double (both dice show the same number) given that the sum of the two dice is 9. 2. **Recall the formula for

1. **State the problem:** We want to find the conditional probability that a card drawn from a standard 52-card deck is a heart, given that the card is red. 2. **Recall the formula

1. **State the problem:** We want to find the conditional probability that a card drawn from a standard 52-card deck is a heart, given that the card is red. 2. **Recall the formula