# Probability Calculations

1) Two cards are drawn from an ordinary deck of 52 cards find the probability of each event showing your reasoning carefully

a. two aces

b. two red cards

c. two red aces

d. two honor cards (A, K, Q, J, 10).

2) A certain airplane has two independent alternators to provide electrical power the probability that a given alternator will fail on a 1-hour flight is .02. what is the probability that

a. both will fail?

b. neither will fail

c. one or the other will fail? show all steps carefully

3) A die is thrown (1,2,3,4, 5, 6,) and a coin is tossed (H, T)

a. enumerate the elementary events in the sample space for the die/coin combination

b. are the elementary events equally likely? explain

#### Solution Preview

Please see attached file

1 two cards are drawn from an ordinary deck of 52 cards find the probability of each event showing your reasoning carefully

a two aces

Total number of cards= 52 cards

Total number of ways of selecting 2 cards out of 52 cards= 1326 =combin (52,2)

where combin (52,2) stands for selecting 2 out of 52 cards

Total number of aces= 4 aces

Total number of ways of selecting 2 aces out of 4 aces= 6 =combin (4,2)

where combin (4,2) stands for selecting 2 out of 4 aces

Therefore, probability of two aces= 0.004525 or 1/221 =6/1326

Answer: 0.004525 or 1/221

b two red cards

Total number of cards= 52 cards

Total number of ways of selecting 2 cards out of 52 cards= 1326 =combin (52,2)

where combin (52,2) stands for selecting 2 out of 52 cards

Total number of red cards = 26 red cards

Total number of ways of selecting 2 red cards out of 26 red cards = 325 =combin (26,2)

where combin (26,2) stands for selecting 2 ...

#### Solution Summary

Answers questions on calculations of probability.