Question

BUSA 3050 Homework 2 Page 2 of 3 3. (5 points) A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events: (a) Let F = the event of getting the white ball twice (b) Let G = the event of getting two balls of different colors (e) Let H = the event of getting white on the first pick. (d) Are F and G mutually exclusive? (e) Are G and H mutually exclusive? 4. (3 points) Helen plays basketball. For free throws, she makes the shot 75% of the time. Helen must now

Answer 1

Solution (a):

P(first ball is white) = and P(2nd ball iswhite) = Now both the given events are independent hence

P(both the balls are white) = (*) =

l

Solution (6)

G = the event of getting two balls of different colors

There are two possibilities - (i)First white and then second Redii First Red and then second white

P(first ball is white) = P(second ball is red) = P(first ball is red) = P(second ball is white) = 5

PG) = P(first ball is white)xP(second ball is red) + P(first ball is red)xP(second ball is white)

111 11 P(G) = 5*5*5*5*2

Solution (c):

P(H) = P(first ball is white)xP(second ball is red) + P(first ball is white)xP(second ball is white)

111 11 P(H) =ཏ*ཏ+ཏ*=2

Solution (d):

Yes, F and G are mutually exclusive events Since these 2 events can not occur at the same time.

first first red white then Both the ball drawn are white then red white These have no common event

Solution (e) :

No, G and H are not mutually exclusive events. Since both have common cases that is first ball is white but second ball is red.

first ball first bal first ball is white is red 2nd ball 2nd ball is red is white white2n d ball is vhite