Answer to Question #144584 in Statistics and Probability for Yosef

Question

Sara downloaded a game on her phone. The objective of this game is to face obstacles with the help of characters which can be of three types: "Earth", "Air" or "Fire".

At the start of each game, Sara randomly obtains the character of one of the three types and may, during the game, keep that character or change the character type only once.

We consider Sara played 10 rounds, taken independently of each other.

The probability that she will get an “Earth” type character is 0.3.

Y designates the random variable which counts the number of characters of type “Earth” obtained at the beginning of the round.

1. Justify that this situation can be modeled by a binomial distribution, where you specify its parameters.

2. Calculate the probability that Sara obtains exactly 3 “Earth” -type characters.

3. Calculate the probability that Sara obtains at least once an “Earth” type character at the start of his games.

Answer 1

1)The probability that she will get an “Earth” type character is 0.3. We can mark this as "success". Therefore, we should use binomial distribution, because the binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times.

2)P(x=3)=C_10,3p³(1-p)^10-3=120*0.3³*0.7⁷=0.2668

3)P(x≥1)=1-P(x=0)

P(x=0)=C_10,0p⁰(1-p)¹⁰=1*1*0.0282=0.0282

P(x≥1)=1-0.0282=0.9718