There are 10 students in a class. 6 of the students are boys and 4 of the students are girls.
Three students are picked at random from the class to form a team. Work out the probability that the team consists of 1 girl and 2 boys.
How do I do this questions, what are the steps? Please show your working out so that I can understand. Thank you!
- Also please don't say anything like C2, C1 etc.. because I really do not know what it means. Thank you!
Three students are picked at random from the class to form a team. Work out the probability that the team consists of 1 girl and 2 boys.
How do I do this questions, what are the steps? Please show your working out so that I can understand. Thank you!
- Also please don't say anything like C2, C1 etc.. because I really do not know what it means. Thank you!
-
You can get 1 girl and 2 boys in 3 separate ways: GBB or BGB or BBG.
For GBB: the probability of choosing a girl first is 4/10.
his means that once she is chosen there are 9 left, 6 of whom are boys. So the first boy's probability is 6/9. This leaves 8 people 5 of whom are boys so the third has probability 5/8.
So the probability GBB is 4/10 x 6/9 x 5/8 which is 120/720, simplifying to 1/6.
In a similar way, BGB is 6/10 x 4/9 x 5/8 = 1/6 and BBG is 6/10 x 5/9 x 4/8 also = 1/6.
Add these to get 1/6 + 1/6 + 1/6 = 3/6 which is 1/2
For GBB: the probability of choosing a girl first is 4/10.
his means that once she is chosen there are 9 left, 6 of whom are boys. So the first boy's probability is 6/9. This leaves 8 people 5 of whom are boys so the third has probability 5/8.
So the probability GBB is 4/10 x 6/9 x 5/8 which is 120/720, simplifying to 1/6.
In a similar way, BGB is 6/10 x 4/9 x 5/8 = 1/6 and BBG is 6/10 x 5/9 x 4/8 also = 1/6.
Add these to get 1/6 + 1/6 + 1/6 = 3/6 which is 1/2