The probability of receiving high dividends on shares at the first enterprise is 0.2, at the second – 0.35

The probability of receiving high dividends on shares at the first enterprise is 0.2, at the second – 0.35, at the third – 0.15. determine the likelihood that a shareholder holding shares in all enterprises will receive high dividends: a) at all enterprises, c) at least at one enterprise

Probabilities of receiving high dividends:
p1 = 0.2; p2 = 0.35; p3 = 0.15.
Probabilities of not receiving high dividends:
q1 = 1 – p1 = 1 – 0.2 = 0.8;
q2 = 1 – p2 = 1 – 0.35 = 0.65;
q3 = 1 – p3 = 1 – 0.15 = 0.85;
1) The likelihood that the shareholder will receive high dividends on the shares of all enterprises:
P (3) = p1 p2 p3 = 0.2 0.35 0.15 = 0.0105.
2) Probability of event A such that the shareholder will not receive high dividends on any shares:
P (A) = q1 q2 q3 = 0.8 0.65 0.85 = 0.442.
The probability of an event opposite to A is such that the shareholder will receive dividends on shares of at least one enterprise:
P` (A) = 1 – P (A) = 1 – 0.442 = 0.558.
Answer: 1) at all enterprises 0.0105; 2) at least one 0.558.