Question

ino1tProbability and Statistics Othman Alahmadi 9/28/17:301PM Test: Test_01 (STAT-3110) Time Remaining: 01:03 49 Submit Test 17 This Question: 3 pts 10 of 22 (11 complete) ▼ This Test: 75 pts possible 17 es tossing a pair of dice, one green and one red, and recording the numbers that come up. If x equals the outcome on the green die and y the at a number less than 3 comes up on the green die. Assume that all elements of the sample space are equally likely to 17 6 occurs on either die. Event C is the event th space S consists of all the possible ordered pairs (x.y) Event A is the event that the sum is less than 6. Event B is the event that a occur. Complete parts (a) through (c) below 囲Click the icon to view the sample space (a) Find the probability of event A PA-□(Type an integer or a simplified fraction ) b) Find the probability of event C P(C)-□(Type an integer or a simplified fraction ) (c) Find the probability of event An c. P(A n C) = □ (Type an integer or a simplified fraction.) om om /17 | pm Sample Space pm (2,1) 22)(23)(24) (25) (2.6) ' | 120n om (4.1) 42) 43) (44 (4.5) (4.6) (5,1) (52) (53) 5.4) (65)(5.6) (6.1 (62)63(6,4)(6.5) (6,6) 120m pm PrintDone 120mi pm Enter your answer in each of the answer boxes 120mir

Answer 1

We have total 36 sample space. Let's talk about the each part one by one.

Part a.) The probability of event A (P(A)) - Event - Sum is less than 6, Number of ways it can be possible is 10 -> [ (1,1), (1,2), (1,3), (1,4), (2,1),(2,2), (2,3), (3,1), (3,2), (4,1) ] so the probabilty is [ Number of ways an event can happen / sample space) so answer is (10 / 36 = 0.278) ].

Part b.) The probabilty of event C (P(C)) - Event - A number less than 3 comes up on the Greed dies, Number of ways it can be possible is 12 -> [ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) ] so the probabilty is [ Number of ways an event can happen / sample space) so answer is (12/ 36 = 0.333) ].

Part c.) The probability of event A$\cap$C (P(A$\cap$ C)) - Event - According to the statement the event here is sum for both dies must be less than 6 and 3 comes up on the green dies, Number of ways it can be possible is 7-> [ (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3) ] so the probability is [ Number of ways an event can happen / sample space) so answer is (7/ 36 = 0.194) ].