ahmad gives his friend juana a lottery ticket for her birthday. the ticket cost ahmad $1, and the back of…

ahmad gives his friend juana a lottery ticket for her birthday. the ticket cost ahmad $1, and the back of the ticket says, \the overall odds of winning a prize with this ticket are 1 : 50, and the expected return for this ticket is $0.50.\ ahmad says, \if 1,000 people each bought one of these tickets, theyd have spent $1,000 in total and get back about $5,000.\ juana says, \the probability that one of these tickets wins a prize is 0.50, on average.\ whose statement is correct based on the expected value? choose 1 answer:

ahmad gives his friend juana a lottery ticket for her birthday. the ticket cost ahmad $1, and the back of the ticket says, \the overall odds of winning a prize with this ticket are 1 : 50, and the expected return for this ticket is $0.50.\ ahmad says, \if 1,000 people each bought one of these tickets, theyd have spent $1,000 in total and get back about $5,000.\ juana says, \the probability that one of these tickets wins a prize is 0.50, on average.\ whose statement is correct based on the expected value? choose 1 answer:

Answer

Explanation:

Step1: Comprender la relación entre probabilidad y valor esperado

El valor esperado $E(X)$ de una variable aleatoria en un juego de azar se define como $E(X)=\sum_{i}x_ip_i$, donde $x_i$ son los posibles resultados y $p_i$ son sus probabilidades correspondientes. Los odds de ganar son $1:50$, lo que significa que la probabilidad de ganar $p=\frac{1}{1 + 50}=\frac{1}{51}\approx0.0196$. El valor esperado del boleto es de $0.50$ dólares y el costo del boleto es de $1$ dólar.

Step2: Analizar la afirmación de Ahmad

Si 1000 personas compran un boleto cada una, el gasto total es $1000\times1 = 1000$ dólares. El valor esperado por boleto es $0.50$ dólares, entonces el retorno esperado total es $1000\times0.50=500$ dólares, no $5000$ dólares. Así que la afirmación de Ahmad es incorrecta.

Step3: Analizar la afirmación de Juana

El valor esperado no es la misma cosa que la probabilidad de ganar. La probabilidad de ganar según los odds $1:50$ es $\frac{1}{51}\neq0.50$. Así que la afirmación de Juana es incorrecta.

Answer:

Ninguna de las dos afirmaciones es correcta.