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Precalculus

Course: Precalculus > Unit 8

Lesson 2: Multiplication rule for probabilities

Interpret probabilities of compound events

A standard deck of 52 cards has 13 clubs, 13 diamonds, 13 hearts, and 13 spades.

Suppose that Anya is going to draw 2 cards without replacement. Here are some events and their meanings:

Event	Meaning
H, start subscript, 1, end subscript	The first card is a heart.
H, start subscript, 2, end subscript	The second card is a heart.
H, start subscript, 1, end subscript, start superscript, C, end superscript	The first card is not a heart.
H, start subscript, 2, end subscript, start superscript, C, end superscript	The second card is not a heart.

Consider this probability:

P, left parenthesis, H, start subscript, 1, end subscript, start text, space, a, n, d, space, end text, H, start subscript, 2, end subscript, right parenthesis, equals, P, left parenthesis, H, start subscript, 1, end subscript, right parenthesis, dot, P, left parenthesis, H, start subscript, 2, end subscript, \mid, H, start subscript, 1, end subscript, right parenthesis

What does P, left parenthesis, H, start subscript, 1, end subscript, start text, space, a, n, d, space, end text, H, start subscript, 2, end subscript, right parenthesis represent in this context?

(Choice A)
The probability that neither card is a heart.
(Choice B)
The probability that both cards are hearts.
(Choice C)
The probability that the first card is a heart given the second card is a heart.
(Choice D)
The probability that the second card is a heart given the first card is a heart.

Stuck?

Precalculus

Course: Precalculus > Unit 8

Problem