Question

Use the complement rule:
1) What is the probability of not drawing a 10 or a spade? Let A be the event of drawing a 19. Let B be the event of drawing a spade.

2) If five coins are flipped, what is the probability of obtaining at least one head?

Answer 1

1)

compliment rule,

P(no X) = 1- P(X)

Let A be the event of drawing a 10. Let B be the event of drawing a spade.

total cards =52

P(drawing a 10 or spade) = P(A U B) = P(A)+P(B) - P(A n B) = 4/52 + 13/50 - 1/52 = 16/52 = 4/13

P(not drawing a 10 or a spade) = 1 - P(A U B) = 1 - 4/13 = 9/13

2)

P(head) = P(tail) = 0.5

P(no head) = P(all tail) = 0.5*0.5*0.5*0.5*0.5=0.03125

P(at least one head) = 1 - P(no head) = 1 - 0.03125 = 0.96875