Here's the question:
A bag contains 5 blue balls and 10 balls of other colours. The balls are indistinguishable except for their colour. A trial consist of drawing a ball at random from the bag, noting its colour and replacing it into the bag. A game is played by performing 10 trials in all. The player receives $0.50 for every blue ball drawn in a game, and receives nothing if balls of other colours are drawn.
At the start of each tournament, each player plays the game once. Players who earn more than $k proceeds to the next round. Find the least value of k such that, in a random sample of 10 players, the probability of all 10 players proceeding to the next round is below 0.1.
I can tell that this is question on binomial distribution, but I can't figure out how to approach it. Would appreciate if someone can help! Thanks in advance!
A bag contains 5 blue balls and 10 balls of other colours. The balls are indistinguishable except for their colour. A trial consist of drawing a ball at random from the bag, noting its colour and replacing it into the bag. A game is played by performing 10 trials in all. The player receives $0.50 for every blue ball drawn in a game, and receives nothing if balls of other colours are drawn.
At the start of each tournament, each player plays the game once. Players who earn more than $k proceeds to the next round. Find the least value of k such that, in a random sample of 10 players, the probability of all 10 players proceeding to the next round is below 0.1.
I can tell that this is question on binomial distribution, but I can't figure out how to approach it. Would appreciate if someone can help! Thanks in advance!