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On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is \(0.5 .\) If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.

Consider the following events for a college student selected at random: \(A=\) student is female \(B=\) student is majoring in business Translate each of the following phrases into symbols. (a) The probability the student is male or is majoring in business (b) The probability a female student is majoring in business (c) The probability a business major is female (d) The probability the student is female and is not majoring in business (e) The probability the student is female and is majoring in business

Probability Estimate: Wiggle Your Ears Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about \(13 \%\) of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).

You roll two fair dice, a green one and a red one. (a) Are the outcomes on the dice independent? (b) Find \(P(5 \text { on green die and } 3\) on red die ). (c) Find \(P(3 \text { on green die and } 5\) on red die ). (d) Find \(P[(5 \text { on green die and } 3 \text { on red die) or }(3 \text { on green die and } 5\text { on red die)]. }\)

(a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? (b) Assign probabilitics to the outcomes of the sample space of part (a). Do the probabilities add up to \(1 ?\) Should they add up to \(1 ?\) Explain. (c) What is the probability of getting a number less than 5 on a single throw? (d) What is the probability of getting 5 or 6 on a single throw?

You roll two fair dice, a green one and a red one. (a) What is the probability of getting a sum of \(7 ?\) (b) What is the probability of getting a sum of \(11 ?\) (c) What is the probability of getting a sum of 7 or \(11 ?\) Are these outcomes mutually exclusive?

Involve a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: \(2,3,4,5,6,7,8,9,10,\) Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four \(10 \mathrm{s},\) etc., down to four \(2 \mathrm{s}\) in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find \(P(3 \text { on } 1 \text { st card and } 10 \text { on } 2 \text { nd })\) (c) Find \(P(10 \text { on } 1 \text { st card and } 3 \text { on } 2 \text { nd })\) (d) Find the probability of drawing a 10 and a 3 in either order.