A die is rolled 5 times. What is the chance of at least 1 ace (1 spot )?A deck of cards has 12 face cards. Suppose we deal 2 cards after shuffling the deck well. What is the probability that the first card dealt is a face card, followed by a non-face card?A fair coin is tossed five times in a row. What is the probability of getting at least 1 head and at least 1 tail?Suppose A and B are two events with P(A) = 0.4, and P(A ? B) = 0.7, (2 points each)(a) For what value of P(B) would A and B be independent?(b) Are A and B also mutually exclusive, if they are independent? Explain.(c) Suppose now that P (B) = 0.6. What would P (A ? B) be?A wildlife biologist examines frogs for a genetic trait that he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research has established that this trait is usually found in 1 of every 8 frogs. He collects and examines 12 frogs. If the frequency of the trait is not changed, what is the probability that he finds the trait in at least 2 frogs?
