Question

In a game called heads, a player tosses a coin three times. S/he wins N$300 if 3 heads occur, N$200 if 2 heads occur, and N$100 if 1 head occurs. On the other hand, S/he loses N$1500 if no head occurs. Let Y be a random variable denoting the player's gain (or loss). The coin is biased such that the probability of landing heads up is 2/3.

a) Find the probability distribution of Y

b) Hence, or otherwise, find the expected value of Y. Interpret your answer.

2. The probability that a patient recovers from a rare blood disease is 0.7. Suppose 13 people are known to have contracted this disease. Calculate the probability that 7 patients will not recover from the disease.

Answer 1

rh ho o stŁ'O) +(80) El pit out of 13 not recover) = 1-0,7 recover) = p(Not 0.3. 6 士乙 7hhh = DOET = QODE: tz | Xoos) — 7 X001 + + X0051 - Xool + 18000 + 8x oog = 27 Th=0 sh 3 = (1 119) __* = ☆ Y (A4m 0051== p) e dim 001 = E M BOC 81. Y= 300 w.p. ( 2 ) ² = 8