Answer:
A) 0.24
B) The probability mass function of X, the number of hits required to break the piñata
X | P(X)
0 | 0.00
1 | 0.70
2 | 0.24
3 | 0.054
4 | 0.006
Step-by-step explanation:
Probability of Sophia breaking the piñata on the first attempt = 0.7
Probability of Sophia NOT breaking the piñata on the first attempt = 1 - 0.7 = 0.3
Probability of Sophia breaking the piñata on the second atrempt = 0.8
Probability of Sophia NOT breaking the piñata on the second atrempt = 1 - 0.8 = 0.2
Probability of Sophia breaking the piñata on the third atrempt = 0.9
Probability of Sophia NOT breaking the piñata on the second atrempt = 1 - 0.9 = 0.1
Probability of Sophia breaking the piñata on the fourth attempt = 1.0 (this is the highest number of attempts as a probability 1.0 means that the piñata breaks on the fourth attempt if it hasn't broken by now)
A) The probability that Sophia does not break the piñata on the first hit and does break the piñata on the second hit.
The required probability = (Probability that Sophia does not break the piñata on the first hit) × (Probability that Sophia does break the piñata on the second hit)
= 0.3 × 0.8 = 0.24
B) Let the random variable X represent the number of hits required for Sophia to break the piñata. Complete the probability distribution of X in the table below Probability of x 0.7
- X = 0, P(X) = 0
- X = 1
Probability of Sophia breaking the piñata on the first hit = 0.7
- X = 2
Probability of Sophia not breaking the piñata on the first hit, but breaking it on the second hit = 0.3 × 0.8 = 0.24
- X = 3
Probability of Sophia not breaking the piñata on the first and second hit, but breaking it on the third hit = 0.3 × 0.2 × 0.9 = 0.054
- X = 4
Probability of Sophia not breaking the piñata on the first, second and third hit, but breaking it on the fourth hit = 0.3 × 0.2 × 0.1 × 1.00 = 0.006
The probability mass function is then
X | P(X)
0 | 0.00
1 | 0.70
2 | 0.24
3 | 0.054
4 | 0.006
To check of we are correct, the probabilities should sum up to give 1.0
The cumulative probability
= 0.00 + 0.70 + 0.24 + 0.054 + 0.006 = 1.00
Hope this Helps!!!!
