Question

An experiment has four equally likely outcomes: E1, E2, Es, and E.Round your answers to three decimal places. a. What is the probability that E occurs? .25 b. What is the probability that any two of the outcomes occur (e.g., E1 or Es)? 375 c. What is the probability that any three of the outcomes occur (e.g., E1 or E2 or E4)?

Answer 1

Answer:

a. 0.25

b. 0.50

c. 0.75

Step-by-step explanation:

P(E1) = 0.25

P(E2) = 0.25

P(Es) = 0.25

P(E) = 0.25

a. Since there are 4 outcomes with the same probability of occurring, the probability of E occurring is:

$P(E) = \frac{1}{4}=0.25$

b. The probability of any two outcomes occurring is twice the probability of a single outcome occurring

$P(two\ outcomes) = 2*P(one\ outcome) = \frac{2}{4}=0.50$

c. The probability of any three outcomes occurring can be written as 100% minus the probability of the remaining outcome occurring

$P(three\ outcomes) = 1-P(one\ outcome) = 1-\frac{1}{4}=0.75$