Question

Please help me with this problem asap thanks

preview answers Remaining time: 32:47 (min:sec) Problem 13. (20 points) Suppose a bag contains many marbles, 49% of which are brown. You draw 5 marbles from the bag with replacement. (10 points each) (a) Find the probability that you draw exactly 2 brown marbles. 0 0.093 O 0.318 O 0.714 O 0.993 (b) Find the expected value of the number of brown marbles. 0 2.45 O 2.81 O 3.79 O 4.77 Note: You can earn partial credit on this problem. preview answers

Answer 1

Solution

Given that ,

a) p = 0.49

1 - p = 1 - 0.49 = 0.51

n = 5

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 2 ) = (₅ C ₂) * (0.49)² * (0.51)³

= 0.3184

Probability = 0.318

b) expected value = n * p = 5 * 0.49 = 2.45