Question

Example 2: We consider 1000 tosses of perfect die. What is the probability of observing 2 heads within these trials? Write the formula for this probability. What is the modus of number of heads observed in those trials?

I think the question is asking about a coin flip and the die is a typo.

Answer 1

ANSWER:

PROBABILITY: Probability is the measure of the likelihood that an event will occur in a Random Experiment. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

We are tossing a perfect coin 1000. probability Now, we have to find observing a heads within P: probability of getting P: Y =0.5 X: Number of heads in the these terials. head in a single trial 1000 terials .: X~ Binomial (n=1000, P=0'5) X heads in this . of observing Probability trials 1000 C ! ; 2-0,1,2,--..100 p(x+2) = $(102) (0-5)100° ; R=0,1,2,..., 1006 p(x ) = ; otherwise p(x=a). § 10) (0-5) 1000; ce= 0.1.2. ---, 10 othercise Normal Approveimation for this probability the formula Number of favorable Oud comes of an event = The probability Total numbee of possible outcomes

P(A)n(e)/n(s) we know, ne) - 1000 nis)- & PA) (09) E(X)= 500 v(x) = npq Hese, Polla .: P+q-1 9-1-16 q = 1/2 v(x)500x -250 X-500 ~N(0,1) 250 The number of head obsequedl in this terials may be any number between olo 1000. For first trial HOS 7, for second torial нт от тн ол ни от тт. Similarly for all trials.