1). Prove that P(EUFUG)= P(E)+P(F)+P(G)- P(E^C F G) - P( E F^c G )- P( E F G^c)-

Question

1). Prove that P(EUFUG)= P(E)+P(F)+P(G)- P(E^C F G) - P( E F^c G )- P( E F G^c)-2P(EFG)

2). A deck of cards contains 30 cards with labels 1,2,.........30 Suppose that somebody is ramdomly dealt a set of 7 cards of these cards( numbered with seven distinct numbers).

a). Find the probability that 3 of the cards contain odd numbers and 4 contain even numbers.

b). Find the probability that each of the numbers on the seven cards ends with a different digit. ( For example , the cards could be 3,5,14,16,22,29,30)

Explanation / Answer

Question 1 is not cleastly written so solving question 2

Question 2 (a) THere are 30 cards number 1 to 30 in the deck of cards. a set of 7 cards are dealt.

(a) There are 15 odd numbers and 15 even numbers so

Pr ( 3 cards are odd and 4 are even) = 15C315C4/ 30C7 = 0.305

(b) Each seven cards have a different digit, that means there are 3 number of 0's, 1's to 9's .

so out of these these 30 last digits, we have to select 7 digits where one digits can't be taken more than 1 times

so probability = (3C1)7 * 10C7 / 30C7 = 262440/ 2035800 = 0.129

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