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Home Question Bank Math Probability Archive 2025 January 12

Probability Questions from Jan 12,2025

Browse the Probability Q&A Archive for Jan 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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10. Considera que en una urna hay una pelota blanca, dos azules, una verde, cuatro amarillas \( y \) contesta. ( Para cada evento \( A \), escribe el evento \( B \) complementario y su probabilidad. - Evento \( A=\{ \) extraer una pelota amarilla \( \} \) - Evento \( B= \) \( P(B)= \) - Evento \( A=\{ \) extraer una pelota azul o una blanca \( \} \) - Evento \( B= \) \( P(B)= \) ( \( A \) partir de la probabilidad de cada evento \( A \), da un ejemplo de un evento complementario \( B \). - \( P(A)=0.25 \); Evento \( B= \) - \( P(A)=0.75 \); Evento \( B= \) - \( P(A)=0.875 \); Evento \( B= \) Explain how the probability of two independent events occurring together is calculated. If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card? \( \begin{array}{ll}\text { 9. Calcula la probabilidad de cada evento } B \text { a partir de la probabilidad } \\ \text { de su evento complementario } A \text {. } & \\ \begin{array}{ll}\text { - } P(A)=0.8 \rightarrow P(B)= & \\ \text { - } P(A)=13 \% \rightarrow P(B)=15 \% \rightarrow P(B)= \\ \text { - } P(A)=0.25 \rightarrow P(B)= & \\ \text { - } P(A)=1 \rightarrow P(B)=1 \rightarrow P(B)=\frac{7}{8} \rightarrow P(B)= \\ \text { - } & \text { - } P(B)=0.73 \rightarrow P(B)=\end{array}\end{array} \) Explain how the probability of two independent events occurring together is calculated. \( \left|\begin{array}{l}\text { Sharon wants to sit in the back seat } \\ \text { of the bus on the trip to the zoo. } \\ \text { The back seat is the full width of } \\ \text { the bus and seats five students. If } \\ \text { Sharon selects her place on the seat } \\ \text { at random, what is the probability } \\ \text { that she will sit at either end by a } \\ \text { window? }\end{array}\right| \) Eine Urne enthält 3 blaue und 7 rote Kugeln Man zieht nacheinander vier Kugeln ohne Zurückzulegen. a) Sind darunter genau 2 blaue, so gewinnt man \( 10 € \), andernfalls muss man \( 4,20 € \) bezahlen. Lohnt sich dieses Spiel auf lange Sicht? b) Man gewinnt \( 8 € \) bei 2 blauen Kugeln, zahlt aber je Spiel einen Einsatz von \( 2,50 € \). Berechne den zu erwartenden Gewinn (oder Verlust) je Spiel If you flip two coins, what are the possible outcomes for the combined events? \( P ( z > 0.85 ) \) a) Ein \( 2 € \)-Stück ist auf der Rückseite mit einer 3 überklebt. Man wirft die Münze drei- mal und bildet die Augensumme. Berechne den Erwartungswert! b) Durch welche Zahl muss die 3 ersetzt werden, damit man \( E(X)=12 \) erhält?
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