Two cards are drawn from a deck of cards. Determine the probability of each of the following events:P(heart or club) P(heart and club) P(red or heart) P(jack or heart) P(red or ten) P(red queen or...

Two cards are drawn from a deck of cards. Determine the probability of each of the following events:

P(heart or club)

P(heart and club)

P(red or heart)

P(jack or heart)

P(red or ten)

P(red queen or black jack)

Which formulas do I use for which problems?

Asked on by catd1115

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justaguide | College Teacher | (Level 2) Distinguished Educator

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You have to draw two cards from a deck of cards. The probability of an event A and an event B occurring is equal to the product of the probability of the event A occurring and that of the event B occurring. Or P(A and B) = P(A)*P(B)

The probability of event A occurring or event B occurring is the sum of the probability of event A and the probability of event B. P(A or B) = P(A) + P(B).

Let's take the first problem:

P(heart or club)

Determine the number of options that satisfy this: HC, CH, HH, CC

The probability of the first is (13/52)*(13/51), second too is (13/52)*(13/51), third is (13/52)(12/51) and the fourth is (13/52)(12/51)

Add all the four: (13*13 +13*13 +13*12 +13*12)/52*51 = 650/2652

P(heart and club)

Here the number of options we have are HC and CH

This gives the probability as (13*13 + 13*13)/52*51 = 338/2652

Similarly solve for the rest.

Keep in mind if it there is an "or" you have a larger number of possibilities as they get added.

Also keep in mind that when you calculate the individual probabilities, for the second card the total number of cards is 51 not 52.

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