10 A card is selected from a standard card deck Find the pro

10. A card is selected from a standard card deck. Find the probability that the card is a face card or a heart. 11. A die is rolled. Find the probability of rolling a 6 or an odd number. 12. Three events are not mutually exclusive. Find P(A or B or C) given P(A) = 0.40, P(B) = 0.20, P(C) = 0.50, P(A and B) = 0.05, P(A and C) = 0.25. P(B and C) = 0.10, P(A and B and C) = 0.03

Solution

10.
Drawing a card pack of 52 = 52 C 1
P( Drawing a card is face) = 12 C 1 / 52 C 1
P( Drawing a card is Heart) = 13 C 1 / 52 C 1

P( Card is HEart and Face) = 4 C 1 / 52 C 1

P(Card is Heart OR Face) = P( Drawing a card is face) + P( Drawing a card Heart) - P( Card is Heart and Face) = 12 + 13 - 4/ 52 C 1 = 21 C 1 / 52 C 1 = 21 / 52

11.
P( ROlling a dice Occurance ae = { 1,2,3,4,5,6}
P( an Odd number drawn } = {1,3,5} = 3/6
P( Number 6 is drawn } = { 6 } = 1 / 6
P( Either an Odd or 6 } = 3/6+1/6 - 0 = 4/ 6 = 2/3