Complete question:
A coin is biased such that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice.
Answer:
1/2
Step-by-step explanation:
Head is 3 times as likely to occur as tail;
Hence,
Sample space for 2 tosses :
{HH, HH, HH, HH, HH, HH, HH, HH, HH, HT, HT, HT, HT, HT, HT, TT}
Expected probability (E(x)) = Σx*p(x)
P(x) = required outcome / Total possible outcomes
x : __________ 0 ______ 1 _______ 2
p(x) : ________9/16_____6/16_____1/16
Σx*p(x) : 0(9/16) + 1(6/16) + 2(1/16)
= 0 + 6/16 + 2/16
= 0 + 3/8 + 1/8
= 4/8
= 1/2
