Given the table below, answer the questions the following questions: 1. What is the probability that P(X>2)? 2. What is the probability that P(X=4)? 3. What is the probability that P(1<X<3)?
| x | P(x) |
| 1 | 0.15 |
| 2 | 0.35 |
| 3 | 0.40 |
| 4 | 0.10 |
1) To find the probability that P(X > 2), we need to sum the probabilities of all the values of X that are greater than 2.
In this case, the values of X that are greater than 2 are 3 and 4. The probabilities corresponding to these values are P(3) = 0.40 and P(4) = 0.10. To find the probability that P(X > 2), we add these probabilities:
P(X > 2) = P(3) + P(4) = 0.40 + 0.10 = 0.50
So, the probability that P(X > 2) is 0.50 or 50%.
2) Now, to find the probability that P(X = 4), we simply look at the probability corresponding to the value of X = 4, which is given as P(4) = 0.10.
Therefore, the probability that P(X = 4) is 0.10 or 10%.
3) Finally, to find the probability that P(1 < X < 3), we need to sum the probabilities of all the values of X that are between 1 and 3, exclusive.
In this case, the value of X that satisfies this condition is 2. The probability corresponding to this value is P(2) = 0.35.
Therefore, the probability that P(1 < X < 3) is 0.35 or 35%.