A box contains 22 red balls and 33 blue balls. Two balls are selected randomly at a time without replacement. Find the probability that the first ball is red and the second ball is blue.
Question
A box contains 22 red balls and 33 blue balls. Two balls are selected randomly at a time without replacement. Find the probability that the first ball is red and the second ball is blue.
Solution
Para resolver este problema, sigamos los siguientes pasos:
-
Determinar el número total de bolas:
- Hay 22 bolas rojas y 33 bolas azules.
- Total de bolas = 22 + 33 = 55.
-
Calcular la probabilidad de que la primera bola sea roja:
- Hay 22 bolas rojas.
- Probabilidad de sacar una bola roja primero = 22/55.
-
Calcular la probabilidad de que la segunda bola sea azul, dado que la primera bola fue roja:
- Si ya hemos sacado una bola roja, quedan 21 bolas rojas y 33 bolas azules.
- Total de bolas restantes = 54.
- Probabilidad de sacar una bola azul después de haber sacado una roja = 33/54.
-
Multiplicar las probabilidades de los dos eventos:
- Probabilidad de que la primera bola sea roja y la segunda sea azul = (22/55) * (33/54).
-
Simplificar la fracción:
- (22/55) * (33/54) = (2/5) * (11/18) = 22/90.
-
Simplificar aún más la fracción si es posible:
- 22/90 se puede simplificar dividiendo ambos números por su máximo común divisor, que es 2.
- 22/90 = 11/45.
Por lo tanto, la probabilidad de que la primera bola sea roja y la segunda bola sea azul es 11/45.
Similar Questions
A bag contains 3 red balls 5 black balls . Two balls are to be taken at random without replacement, from the bag. Find the probability that the two balls taken are of the same colour.
A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.Choices:- 23/42 19/42 7/32 16/39
In a bag, there are 8 red, 10 blue and 12 green balls. A ball is picked randomly from the bag and 5 blue balls are added to the bag. Now, one ball is picked randomly from the bag. What is the probability that the first ball picked is red and the second ball picked is blue?
A bag contains seven red balls and four yellow balls. If we select two balls at random, what is the probability that both balls will be yellow if this sample is without replacement?
ProbabilityA bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?Options10/215/211/2111/21
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.