Question

The experimentation of a new drug in a lab has two outcomes. The probability of getting the first result is 0.20. The probability of getting second result is 0.80. Let x be the number of the experiment results. Construct a probability distribution for the random variable x. If the experiment is repeated twice find the probability of

a.   Both having First result

b.   One first result and another is the second result

c. Both having the second result

Note : Answer should be in word version format please

Answer 1

a. The probability of getting first results is 0.2 and the probability of getting second result is 0.8. If the experiment is repeated twice the the first experiment can give the first result with a probability of 0.2. The second experiement can also give the first result with a probability of 0.2. Hence the probability of both experiments having first result is 0.2*0.2 = 0.04

b. One first result and another second result can happen in 2 ways. One way is that first experiment gives first result and second experiement gives second result. The probabilites of these are 0.2 and 0.8. Other way is that first experiment gives second result and second experiement gives first result. The probabilites of these are 0.8 and 0.2. Hence the probability of one first result and another is the second result is 0.2*0.8+0.8*0.2 =0.16+0.16 = 0.32

c. If the experiment is repeated twice the the first experiment can give the second result with a probability of 0.8. The second experiement can also give the second result with a probability of 0.8. Hence the probability of both experiments having second result is 0.8*0.8 = 0.64

Thus the probability distribution of x is as below