Question

Question If you toss a fair die four times, what is the probability that you get at most one six? Select one: O a. 0.1319 O b. 0.1667 O c. 0.3333 O d. 0.5683 e. 0.8681

Answer 1

When fair die is tossed, the probability of getting any number is 16 . Probability of getting a six when fair die in rolled = to let x be random variable denotes fair die is lössed four times. number of i'r when n=4 p= X ~ Binomial (n= 4, p = +) The probability man function of xing P(x=x) = (46) *C.-) ; x = 0,1,2,3,4. Here, we need to find PCX CD 4.2 P( x4)= P(xco) + P(x=1) 3 (4)(+) (3) + (4) (+)(3) 0.482253086 42 + 0.3858024 6914 0.86805555556 0-8681 ie Option @ 2) Here, The number of trials is fixed, sie n=03 Since marbles are drawn with replacement, the outcome of any Trial does not affect the outcome of others. -> Each Trial results in one of the two outcomes called success and failure (ie obtaining green marble or not obtaining green marble)

The probability of success, ie probability of obtaining green marble remains the same from Trial to trial ( since done with replacement). Since all four conditions ave satisfied, x have Binomial distribution. Option ③ Yes. 3) Given, XNN (0,1) first, we need to find plx<0.41) P(x<0.41) = P(Z<0.41) = 0.659097 [from standard Normal lable Now, n= 3 P = o. 659097 YN Binomial (n=3, p=0.659897) man function of Yes, PCY= y) = (3) (0.659097) (-0.659097) ;y=0, 1,2,3 Here, we need to find Ply=2) P(Y= 2) = (3) (0.6590975 (1-0.659097) The probability y 3-4 2 0.444273 84 611 o. 4 4 4 3 1.e option d