# Probability of dice, coin flips, and deck of cards.

1. A die is tossed 7 times, find the chance that

(a) all rolls show 2 or less

(b) none of the rolls show 2 or less

(c) not all show 2 or less

2. A coin is tossed 4 times, find the chance that

(a) all rolls are Heads

(b) the 1st two tosses are Head and last two are Tails

(c) the 4th is a Head, given the 1st 3 are tails

3. 3 cards are dealt from a well-shuffled deck. Find the chance that you get 2 Reds followed by the King of Spades

4. 4 cards are drawn from a well-shuffled deck. Find the chance that you get all four 6's.

5. A die is tossed 4 times. Find the chance that you get a six on the 1st toss and a two on the others.

Please work each problem ot showing all of the work!

#### Solution Preview

1. A die is tossed 7 times, find the chance that

(a) All rolls show 2 or less

There are 6 outcomes on a pair of dice. Each roll is independent of other rolls. On a single roll, 2 of the six outcomes are two or less, so on a single roll the probability is 2/6 or 1/3. The probability that 7 consecutive rolls show a 2 or less is 1/3 to the seventh power or:

P = (1/3) (1/3) (1/3) (1/3) (1/3) (1/3) (1/3)

(b) None of the rolls show 2 or less

The probability of not rolling a 2 or less on a single roll is (2/3). The probability of not seeing this on 7 consecutive rolls is:

P = (2/3) (2/3) (2/3) ...

#### Solution Summary

The solution shows how to calculate probabilities when rolling dice, flipping a coin, and drawing from a deck of cards.