1) A coin is biased so that the head is 3 times as likely to occur as tail.If the coin is tossed twice,find the probability distribution of number of tails.
2) What is the differnce between 'with replacement" and "without repalcement&
1) Probability of getting a Head = 3/4
Probability of getting a Tail = 1/4
The coin is tossed twice, total number of possible outcomes are [HH,HT,TH,TT]
The probability distribution of number of tails is:
|Outcome||1 Tail||2 Tails||No Tail|
2) 'With replacement' means when we put back the first outcome and 'without replacement' means that we don't put back the first outcome.
(1) When we sample with replacement, the two sample values are independent.
(2) In sampling without replacement, the two sample values aren't independent.
A circle is of radius 8 units. Then the probability that a randomly chosen point inside the circle is
closer to the centre than the circumference, is