1. Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Similarities and Differences in a Random Sample of 375 Married Couples

Number of Similar Preferences Number of Married Couples

All four 29

three 133

two 113

one 64

none 36

Suppose that a married couple is selected at random.

(a)Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (For each answer, enter a number. Enter your answers to 2 decimal places.)

0-

1-

2-

3-

4-

(b)Do the probabilities add up to 1? Why should they?

Yes, because they do not cover the entire sample space.

No, because they do not cover the entire sample space.

Yes, because they cover the entire sample space.

No, because they cover the entire sample space.

What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common

1, 2, 3, 4 personality preferences in common

0, 1, 2, 3, 4, 5 personality preferences in common

0, 1, 2, 3, 4 personality preferences in common

2) Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

=22;=3.6

P(x30) =

3)Assume thatxhas a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

=4;=6

P(1x10) =

4) The following question involves 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 10s, etc., down to four 2s 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?

Yes. The events can occur together.

No. The probability of drawing a specific second card depends on the identity of the first card.

No. The events cannot occur together.

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

(b)FindP(ace on 1st cardandqueenon 2nd). (Enter your answer as a fraction.)

(c)FindP(queenon 1st cardandace on 2nd). (Enter your answer as a fraction.)

(d)Find the probability of drawing an aceandaqueenin either order. (Enter your answer as a fraction.)