Question

In: Statistics and Probability

1. Given P(A) = 0.3 and P(B) = 0.2, do the following. (For each answer, enter a...

1. Given P(A) = 0.3 and P(B) = 0.2, do the following. (For each answer, enter a number.)

(a) If A and B are mutually exclusive events, compute P(A or B).

(b) If P(A and B) = 0.3, compute P(A or B).

2. Given P(A) = 0.8 and P(B) = 0.4, do the following. (For each answer, enter a number.)

(a) If A and B are independent events, compute P(A and B).

(b) If P(A | B) = 0.1, compute P(A and B).

3. 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?

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

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

No. The events cannot occur together.

Yes. The events can occur together.

(b)Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.)

(c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.)

(d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.)

4.

You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck.

(a)Are the outcomes on the two cards independent? Why?

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

Yes. The events can occur together.

No. The events cannot occur together.

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

(b) Find P(ace on 1st card and king on 2nd). (Enter your answer as a fraction.)

(c) Find P (king on 1st card and ace on 2nd). (Enter your answer as a fraction.)

(d)Find the probability of drawing an ace and a king in either order. (Enter your answer as a fraction.)

Expert Solution

orchestra answered 1 year ago

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