Question

In: Statistics and Probability

Prob 1 Using a standard deck of cards, calculate the following probabilties. (denote your answers in...

Prob 1 Using a standard deck of cards, calculate the following probabilties. (denote your answers in decimals) a) drawing

a) red queen

b) drawing two red queens

c) drawing a diamond or a king

d) drawing a red card or a black card

e) Are queens and kings mutually exclusive?

Expert Solution

N = number of cards in a standard deck = 52.

Number of king cards = 4

Number of queen cards = 4

Number of red cards = 26

Number of black cards = 26.

Number of diamond cards = 13

Number of king cards = 4

Number of red queens = 2

a) P ( drawing a red queen ) = 2 / 52 = 1/26

b ) P ( drawing two red queen ) = ²C₂ / ⁵²C₂ = 1/1326=0.00075

c) A : drawing a diamond

P( A ) = 13/ 52 = 1/4

B: Drawing a king card

P ( B) = 4/52 = 1/13

P(Drawing a king of diamond) = = 1/52.

P ( drawing a diamong or king card ) = P ( A U B)

P( Drawing a diamond or a king) = 0.3076

d) C : drawing a Red Card

P ( Drawing a Red Card)= P ( C) = 26/52. =0 .5000

D : drawing a Black card

P (Drawing a black cards) = P(D) = 26/52 = 0.5000

Since C and D are mutually exclusive events.

P ( Drawing a red or a black card) = P ( C U D ) = P(C) + P(D)

= 0.5000 + 0.5000

= 1

P ( Drawing a red or a black card) = 1

e) E : drawing a king card

P ( E ) = 4 / 52 = 1/13

F : drawing a queen card

P(F) = 4/52 = 1/13.

Hence E and F are mutually exclusive.

orchestra answered 1 year ago

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