Pregunta
A box contains 7 letters, shown as CHARTED. What is the probability of the outcome RAT in that order if 3 letters are drawn one by one (a) with replacement? (b) without replacement? The probability of the outcome RAT in that order if 3 letters are drawn with replacement is (Type your answer as a fraction.)
Ask by Medina Cole. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The probability of drawing RAT in order with replacement is 1/343.
Solución
We have 7 letters in the box (C, H, A, R, T, E, D), and each letter is equally likely to be chosen.
For drawing with replacement:
• The probability of drawing "R" on the first draw is 1/7.
• The probability of drawing "A" on the second draw is 1/7.
• The probability of drawing "T" on the third draw is 1/7.
Since the draws are independent, multiply the probabilities:
(1/7) × (1/7) × (1/7) = 1/343
Thus, the probability of the outcome RAT in that order when drawing 3 letters with replacement is 1/343.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
When drawing with replacement, the probability of getting each letter is independent. There are 7 letters in total, so the probability of drawing 'R' first is 1/7, 'A' second is also 1/7, and 'T' third is again 1/7. Therefore, the probability of the outcome "RAT" in that order is: (1/7) * (1/7) * (1/7) = 1/343. Now, for without replacement, when you draw 'R' first, you remove it from the box, leaving 6 letters. So the probability for 'R' is again 1/7, but then 'A' will have a probability of 1/6 now, and 'T' will be 1/5 on the third draw. Hence, the probability of "RAT" in that order without replacement is: (1/7) * (1/6) * (1/5) = 1/210.
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
